Constant Fire

Rashi:"A continuous fire"
This fire must also be kindled from [the fire] on the outer altar.

"it shall not go out"
[Since "it shall not go out" is stated twice, once in verse 5 and a second time here] anyone who extinguishes the fire on top of the altar transgresses two negative commandments.

Baal HaTurim: The fire was like a ladder for the angels to ascend, as stated in the verse: "The angel of G‑d ascended in the flame of the altar." Similarly, in Ezekiel, "And behold six men...and they stood next to the copper Altar."

Therefore the Outer Altar was made of copper in accordance with the description of the chayot-angels, "They glittered with the color of burnished copper." The inner Golden Altar, by contrast, corresponds to the Shechinah, as implied by the verse: "His hands are rods of gold." Therefore if any blood is brought into the Sanctuary, that sin offering from which it came may not be eaten for the concept of eating does not apply in the higher realms symbolized by the Inner Altar.

Ohr HaChayim: "and the fire of the altar"
These words hint to the many pains we have felt at the hands of the merciless nations who did not pity us, seeing G‑d had already punished us for so many years. The Torah tells us that when the dawn of that morning of redemption comes, G‑d's anger will burn and consume all those who have oppressed us during the many years of our exile and especially the Western nations.

The words "Aish Hamizbayach/the fire of the altar" also hint to the sacrifice of Yitzhak when he lay bound on the altar. The word "Hamizbayach/altar" involves the attribute of Justice that will be aroused and prevail, and this is the secret of the words related to the word "tukad bo/shall burn in it" (lit.). Understand [this].

Maggid Mesharim: Even if sins cause the abundance to diminish, nevertheless there will [always] be some illumination from the flame of the sefirot.

"And the Kohen shall burn wood on it"
The illumination of the flame from the sefirot does not suffice; the Kohen must burn wood, signifying the sefirot, in order to augment the flame and brighten their illumination.

"every morning"
...so that it will illuminate well. This is the secret of what our Rabbis said that even though fire descends from Heaven, there is a commandment to bring it from an ordinary source.

"He shall prepare the burnt offering upon it"
The Congregation of Israel will rise to bina.

"He shall cause the fat parts of the peace offering to go up in smoke upon it"
White fat hints at the illumination of the sefirot which, when it is burned in fire, becomes red and afterwards returns to being white, in the rising cloud.

"A continuous fire shall be kept burning on the altar"
...the flame and the illumination of the sefirot should never cease. Nevertheless, the flame and the illumination of the sefirot should not cease. For if they ceased, in one moment all the worlds would be destroyed. It draws to it abundance and illumination; therefore, the worlds can continue to exist.

Lubavitcher Rebbe: The mitzvot are given over in 3 instructive modalities: Emor - Talk to the people, Dabayr - Speak to the people, and Tzav - command-connect with the people. These 3 instruction modalities correspond to the 3 lines of power on the Tree of Life.

All the Mitzvot which are associated with the right channel of the tree which cause an expansion of the Divine Outflow down the tree are introduced with the word Emor which has a softness and affectionate quality. All of the Mitzvot which are associated with the left channel of the Tree of Life causing a focusing and detailed compression in the Divine Outflow are introduced by the word Dabayr which has a narrow compacting quality. Finally, all of the Mitzvot that are associated with the center channel of the Tree of Life causing an inner revelation connecting the upper and lower poles of Divine Outflow are introduced by the word Tzav which has a quality of bringing together opposites. Their effect on each kind of Mitzvah on the soul involving itself in their performance corresponds to their effect on the Power lines of the Tree of Life.

Zohar Tzav 28 Rayah Mehemna:
"The fire shall ever be burning upon the altar...". This is the Torah, of which it says: "'Is not My word like a fire?' says G‑d". (Jeremiah 23:29) "It shall never go out"; (Lev. 6:6) surely, since a transgression does not put out the Torah. But a transgression puts out a precept, and he who commits a transgression puts out a precept, which is 'a candle'. He thus puts out his candle from his own body of which it says: "A man's soul is the candle of G‑d". (Prov. 20:27) It is extinction indeed, for the body remains in darkness. He who causes the Shechinah to go away from Her abode, brings about extinction and darkness into that place. A transgression is darkness, "and a handmaid that is heir to her mistress," (Prov. 30:23)
A transgression is darkness...
Regarding the ascension of a precept on the side of the common people - for them it extinguishes a precept. The words: "And the wicked shall be silent in darkness," (I Samuel 2:9) are fulfilled in them. As for the Sages of the Torah, is never extinguished because they shine upon the precept with several mysteries of the Torah. For light is called 'a secret/Raz'. The precepts of the Torah, which the Sages observe, are considered in them to be just like the Torah. They will never be extinguished, night or day, because they observe in relation to her: "But you shall meditate therein day and night". (Joshua 1:8)

The smoke coming up from the mouths with words of the Torah is like the smoke of the wood set on the altar. She is set for Her husband. This is so in the verse: "When you light ('raise') the candles," (Num. 8:2) as it says of them: "To cause ('raise') the candle to burn always". (Ex. 27:20) By the smoke from the wood and the cloud of incense of which the Torah is the smoke will awaken in the heart, to chochma that resembles the brain.