The Final Mission

Rashi: "against the Midianites"
But not against the Moabites, for the Moabites were involved in the matter out of fear, since they were afraid of being plundered by them, because all it says is, "do not provoke them into battle" (Deut. 2:9) but the Midianites were angered over a dispute which did not concern them. Another interpretation: Because of the two good doves [virtuous proselytes] whom I have [in mind] to bring forth from them, [namely] Ruth the Moabitess and Na'ama the Ammonitess.

Baal HaTurim: "Take vengeance for the children of Israel"
...vows should be made in a time of distress or war. This passage is juxtaposed with the passage concerning the vows, to indicate to you that vows should be made in a time of distress or war. Also, when a man remains silent regarding the vows of his daughter or his wife and does not defer their vows for them, he stands in their stead. If so, the Midianites who caused Israel to sin will certainly be punished.

"Afterward you will be brought in"
Whereas Moses witnessed the incident of the Midianitess and did not act zealously on G‑d's behalf, his life was made dependent on exacting vengeance from the Midianites.

"Unto your people"
The word "amecha" is spelled with a Yud (= 10) in the plural form to indicate to you that ten different places Scripture mentions the death of Moses.

Ramban: The commandment was given to Moses for his honor, and Moses showed honor to Pinchas because the latter had begun the meritorious task of punishing Midian by killing Cozbi. It was up to Moses to finish it, so he appointed Pinchas as the anointed priest for war. It was not fitting for Elazar to do so for he was the High Priest after the death of Aaron.

Ohr HaChayim: Moses could not die without rehabilitating his people spiritually. His soul would not be able to enter the World to Come with peace of mind. According to the kabbalists, the place one occupies in his mind in the hereafter while awaiting judgment is called "Amav/his people". G‑d told Moses that he could not die peacefully until he had rehabilitated himself by organizing the punitive expedition against Midian. Once he did this, he could die without facing an accuser after his death. This was a great kindness that G‑d did for Moses.

The Lubavitcher Rebbe: According to Chasidic thought, the war against the 7 Canaanite nations alludes to the battle of refining one's overtly undesirable traits which fall into 7 broad categories, stemming from the 7 emotional faculties of the animal soul. In contrast, the war against Midian involved fighting against a subtle type of evil which is found in virtually every personality, even those who dedicate themselves as full time "ministers" of G‑d. Thus, even the Levites and those among the Jewish people who devote themselves "to stand before G‑d and serve as His minister" must participate in waging the spiritual war against Midian.
...a lack of unity and camaraderie...arises from a sense of overinflated self-importance...
What is the "subtle evil" that can plague even the most dedicated servant of G‑d? Chasidic thought says that this is a lack of unity and camaraderie between one man and another, indicating underlying emotions of divisiveness and unjustified hatred. All this arises from a sense of overinflated self-importance, which causes a person to be intolerant of others and eventually view them as enemies. Clearly the war against these attributes is very important indeed!

Zohar Balak 189:
Come and see that everything stemmed from Midian; the thrust of their counsel was about Moses, and with the advice of Midian they hired Balaam. When they realized that Balaam was incapable, they followed another wicked idea, and they freely offered their women and daughters even more than Moab. About the women of Midian, it is written: "Behold, these caused the children of Israel." (Num. 31:16) Everything stemmed from Midian. They took counsel with their chief that he should let loose his daughter, since they were plotting to ensnare Moses in their net. They adorned her with how many spells, so she should successfully catch the heads.

Yet the Holy One, blessed be He "turns wise men back". (Isaiah 44:25) They envisioned that the head would be caught in their net, yet they did not know. They saw, yet saw not. They had a vision that the chief of the people would fall for her, and several thousand others. They thought it would be Moses, so they let her loose, and gave her orders about Moses, so that she should not couple with another but only with him. She asked them, 'How will I be able to tell him apart?' They said to her, The one that you'll notice, that everyone stands up before, you will engage yourself with him and with nobody else. Once Zimri son of Salu came, 24,000 people from the tribe of Shimon stood up in his honor, since he was their chief. She assumed that he was Moses and she united with him. When all those 24,000 saw this, they carried on with whatever they saw fit and that was the cause of everything that happened after that.
David came and washed clean the pot from their filth...
Everything originated in Midian in several ways. Therefore, Midian was punished and the Holy One, blessed be He, said to Moses, "Execute the vengeance of the children of Israel on the Midianites". (Num. 31:2) For you, it is appropriate and becoming. As for Moab, I leave them alone until the two jewels will come out from among them. Here's David son of Yishai who will take revenge on Moab, and will rinse the loaded pot of filth from Pe'or. This is what it says, "Moab is my washpot" (Ps. 60:10) assuredly. As long as these two jewels did not come out of there, they were not punished. As soon as they emerged, David came and washed clean the pot from their filth, and all received their punishment, Midian during the time of Moses and Moab during the time of David.

Come and see that, in spite of all this, the wicked of Midian did not desist from all their evil. Generations later, when they saw that Joshua had died, together with all the elders who were worthy to have miracles caused through them, they figured that the time was now opportune. What did they do? They approached Amalek and told them, It is worth it for you to remember what the children of Israel and their master Moses and his disciple Joshua have brought upon you that will destroy you from the world. Now is the opportune time, for they have no one to shield them. We will go and accompany you, as is written: "Midian and Amalek and the children of the east..." (Judges 6:33) "And because of Midian the children of Israel made for themselves the tunnels..." There was no one in the world who wished to harm the children of Israel like Midian. You might say Amalek; because of jealousy of the covenant, they approached the covenant. Therefore, the Holy One, blessed be He, took everlasting vengeance, which was not to be forgotten.