A Portal to History

Rashi: "Pinchas the son of Elazar the son of Aaron the kohen"
Since the tribes were disparaging him, saying, Have you seen the son of Phuti, whose mother’s father [Jethro] fattened calves for idol worship (Exod. 6:25, Rashi) and who killed a chieftain of an Israelite tribe? For this reason, Scripture traces his pedigree to Aaron.

"by his zealously avenging Me"
"by his avenging My vengeance," by his releasing the wrath that I should have released. The term 'kin'a' always denotes someone angered to take vengeance for some matter.

Targum Yonatan: Moses went, and said to Pinchas, Behold, I give to him... And because they defamed him, saying, Is he not the son of Phuti, the Midianite? Behold, I will make him possess the high priesthood, and because he took the lance with his arm, and struck the Midianitess in her body, and prayed with his mouth for the people of the house of Israel, the priests shall be worthy of the three sacrificial gifts of the shoulder, the cheekbone, and the innards; and it shall be to him, and to his sons after him, an everlasting covenant of consecration, because he was zealous for the Lord, and propitiated for the children of Israel.

Ramban: The Holy One, Blessed be He here informed Moses that he would give Pinchas a good reward for his zeal. He also commanded Moses to tell Israel that Pinchas would be a priest forever. Scripture does not say "and it shall be for him and to his seed after him, an everlasting priesthood,", as he said about Aaron, but instead it says "the covenant of an everlasting priesthood" and "I will give to him My covenant of Peace," meaning He will give him a covenant of peace cleaving to it, whereas with Aaron it says "for splendor and for beauty". Therefore it says here about Pinchas, "because he was zealous for his G‑d".

Ohr HaChayim: "has turned away my wrath"
The Torah may have mentioned this to teach us that once G‑d's wrath has been aroused it requires a new merit on the part of His creatures to sweeten the attribute of Justice. At the very least we can assume that is what Moses thought. G‑d explained to Moses that in this instance it had been Pinchas' deed which had succeeded in turning away His wrath. The word "turned away" in the causative form teaches that G‑d's wrath did not abate on its own.

"From the children of Israel"
This means that once G‑d's anger had descended upon them, Pinchas successfully removed it from the children of Israel. This is a great compliment to Pinchas, for it caused G‑d personally a sense of wellbeing, seeing that as long as He was angry and jealous it had caused Him sadness and distress.

"and I did not totally consume"
The Torah wanted to show that once G‑d's anger had been aroused at Israel, it could not be turned away without Pinchas doing the following: (1) displaying his personal jealousy on behalf of G‑d, (2) without any ulterior motive (3) and in full view of the entire nation. As far as saving the Jewish nation from total annihilation, perhaps G‑d would have allowed a small portion of Israel to survive even if Pinchas' deed not include the 3 elements above. The prayer of a tzaddik like Moses could have done this. Yet if the Torah had only mentioned that Pinchas turned away G‑d's wrath, without adding that G‑d did not destroy the whole people, perhaps we could conclude that all the action of Pinchas accomplished was to prevent the complete annihilation of the people.

Maggid Mesharim: "I am giving him My covenant of peace and it will be for him and his seed later"
By his deed, Pinchas did 2 good things: (1) he turned back the anger of the Holy One from the Children of Israel and thus brought peace between the two; (2) he avenged the jealously of the Holy One, Blessed be He.

So, the Holy One Blessed be He repaid him for both deeds. Since he brought peace between Israel and their Father in Heaven, it states "Behold I am giving him My covenant of peace." He gave Pinchas for the trait of the covenant, the trait of peace. And because he took vengeance for the Holy One, Blessed be He, G‑d said, "It shall be for him and his offspring after him a covenant of eternal priesthood.", meaning that like him his offspring would be righteous.

He also promised Pinchas that his offspring would continually exist and not be destroyed by any of the decrees or in any of the exiles in the world. And this is hinted in the statement that for his offspring there is a covenant of eternal priesthood. It means that his offspring will exist forever. He also promised him that the High Priesthood would always come from him. This happened during the 1st Temple, that all the High Priests came from Pinchas. In the future, in the time of Mashiach, so too will the high priests come from Pinchas. That is what is meant by "a covenant of eternal priesthood"

"And Pinchas saw"
When Israel sinned, impurity spread out in the world, and therefore Moses and Aaron cried at the opening of the Tent of Meeting, which is the Congregation of Israel, in order to repair them by means of that crying what those evil people blemished.
Pinchas saw that crying was not repairing the blemish...
Pinchas saw that crying was not repairing the blemish though it is somewhat of a deed since the face becomes twisted and there are some who consider a twist of the lips to constitute a deed, but it is not an actual deed to be performed to repair the blemish. So "Pinchas took a spear in his hand" to do a deed with his hand, just as those who carried out the misdeeds actual use their hands to carry them out.

Pinchas rose to perform this deed, as he said, "Aaron is the High Priest, and Elazar is his second-in-command, so I am the one appointed for war. Since nothing has been transmitted to either my grandfather or father concerning war, they are not obligated to start this war. But I who have been appointed for war, must begin this holy obligatory war." Thus, he referred to it after mentioning Elazar and Aaron, as if to say Pinchas saw they were greater, yet this matter has not been placed in their hands, so he understood that it had been given to him for these reasons.

Before Pinchas came and did the deed, the punishment of death did not exist at all, for so was the way of the Other Side. Since there was no death, the Israelites were not aware of the good that Pinchas did for them. So the Holy One, Blessed be He wished to inform them that Pinchas did a great favor in that "he turned back My wrath". 24,000 Israelites died. On this it said, "I did not consume" — that is had Pinchas not acted, impurity would have spread in the world, then He would have destroyed them. So Pinchas returned My anger to its sheath. Yet it is impossible to return a sword empty in the secret of , "if one has a single defending angel" (Job 33:23) and there is atonement in "I have found a ransom," (Ibid. 33:24) thus 24,000 died.

Lubavitcher Rebbe: The tribes thought they had proof that Pinchas did not have good motives [See Rashi above] This teaches us a powerful lesson when we are tempted to find fault in another's good deeds and question their motives: One can never know another's true intentions. So long as a person is doing good, he should not be put down or mocked, even if one has solid proof that one is insincere. And in any case even if it were true, we are always told to study Torah and perform mitzvot even for the wrong reason, since we will eventually come to have pure motives. (Pesachim 50b)

Where does the desire to find fault in people who are doing something good? In our case, the tribe appeared to have holy intentions: They were concerned that Pinchas had slighted Moses' honor by taking the law into his own hands. One must imagine that he has a low tolerance for other people's bad intentions because he himself is humble, and thus he finds the pride of others distasteful. In truth, the opposite is the case. When one criticizes the good deeds of others, it is because the critic is proud and does not like the idea that someone else did well. His arrogance leads him to put the other down, so they do not wound his pride or inspire him to be a better person, which would take work.

Moreover, even if another's mitzvah observance seems haughty, the critic's pride is more distasteful. The person who showed off with his mitzvah was at least honest about his pride and did not attempt to concede it. The critic though cannot tolerate the truth, and he stoops to dishonesty, veiling his pride in a cloak of humility and righteous indignation.
It is much wiser to be an activist than a critic.
It is much wiser to be an activist than a critic. A little pride can make critique destructive, rather than constructive, but a good deed is good regardless of intention. (Likutei Sichot 8:167)

Zohar Pinchas 213:
(Rabbi Shimon said: This verse has in it the secret of wisdom. "You that dwell in the gardens" refers to the Shechinah, which is with Israel in exile and accompanies them in their troubles. "The companions hearken for your voice..." refers to the camps of the higher heavenly hosts, all of whom listen to your voice, the voice of your praises in exile. "Cause me to hear it" is as it is said: "let me see your countenance, let me hear your voice". (Songs 2:14) "Let me hear your voice" refers to the voice of those Colleagues who engage in Torah, for I have no praise such as those who engage in Torah.

Rabbi Shimon said: Apparently at midnight, as the day begins to dawn, all those who are privileged to engage in Torah come with the Queen to welcome the King, and they grow stronger and take possession of the Shechinah. Moreover, a thread of kindness hangs over Him, as the Sages have explained.)

Come and see: Everyone who is privileged to be strengthened in the Shechinah gains protection for himself from those matters that are considered to be opposed. Who is protected? Those who do not falsify by the sign of the Holy Covenant the daughter of a foreign god. And he who watches over himself, as it were, the Assembly of Israel is linked to Him, in turn, and protects him and greets him peacefully. And this is even more so if he has been privileged to zealously take up the cause and guard.

Said Rabbi Shimon: Israel at that time would have deserved to have been extirpated from the world had not Pinchas first done the deed , and thus the anger abated. This is what is said: "Pinchas, the son of Elazar, the son of Aaron the priest, has turned my wrath away". (Num. 25:11)

Come and see: One who is zealous for the Holy Name of the Holy One, blessed be He, even if he is not designated for greatness and is not worthy of it, he earns it and gains it. Pinchas was not worthy at that time, but because he was zealous for the name of his Master, he earned everything and rose to the highest position, and everything was put right within him, and he was privileged to serve in the supreme priesthood. From then on he was referred to as Pinchas the son of Elazar, the son of Aaron the priest, since he completed two stages. And this was because he was zealous for the name of his Master and put the wrong right.