On the Golden Altar

Rashi: for bringing incense up in smoke
to raise smoke up on it, namely the smoke of incense.

BeRahamim LeHayyim: 'Altar' in Hebrew is 'mizbayach,' whose numerical value is 57, equal to the words El Havayeh, meaning "to G‑d", showing how all the KoRBanot/sacrifices offered on the altar with proper intentions are pipelines to KaReiV1/come closer to G‑d.

Ramban: Being that the altar of incense is one of the articles in the inner part of the Mishkan, it should have been mentioned together with the Table and Menorah [in the previous parasha] as was done at the time of mentioning their construction in Parashat Vayakhel (Ibid. 37:25). But the altar and all its vessels is mentioned here to connect it to what G‑d said at the completion of all of the vessels, "And the Tent shall be sanctified by My Glory" (Ibid. 29:43) as well as "I will dwell among the children of Israel." (Ibid. 29:45) so He now said that they had to make an altar to burn incense for the glory of G‑d.

Moses was given a secret, that incense checks the plague... Moses was given a secret, that incense checks the plague, for incense is of the attribute of judgment, as its says, "They will put incense in your nose [in Hebrew, 'B'apecha']" (Deut. 33:10), which is of the same root Ve'charah Api [an expression of anger] (Ex. 22:23). It is for this reason that G‑d said of foreign incense "and before all the people I will be glorified"2 (Lev. 10:3) meaning that they will then known My glory "for He will not pardon your sin" (Ex. 23:21).

Ohr HaChayim: Any part of the Tabernacle which was suitable for use in the Holy Temple in Jerusalem was permitted to be used there on a permanent basis. An exception to this rule was the golden Altar which, despite the fact that its function did not change in the Temple, was nevertheless required to be replaced. This detail was hinted to by the Torah by describing the golden Altar separately here at the end of Parashat Tetzaveh.

Lubavitcher Rebbe: The Hebrew term for sacrifices (korbanot) is related to the word Kiruv meaning "close," as the process of bringing sacrifices in the Temple brings man closer to his Creator. Ironically, the word "close" itself suggests a certain distance. For if 2 entities are merely "close" to each other, they remain in the final analysis separate; they have come close together despite their inherent separateness.

Incense/Ketoret suggests "connecting." [Katar is the Aramaic translation of the Hebrew word Kesher/knot or connection.] Here we are not speaking of 2 separate entities which have become close, but rather of 2 entities that have become one. Thus the offering of the incense in the Holy Temple was a process by which man and G‑d, who had already become close through the offering of sacrifices, were then joined together in total oneness.

In order to stress this point, the command to build the Incense Altar was recorded here, at the end of Parashat Tetzaveh. The Tabernacle had been erected, the Priests inaugurated, and G‑d's presence rested in the Tabernacle. (Ibid. 25-29) Nevertheless G‑d was only close to the Jewish people and not one with them (in a revealed manner) until the incense was offered.

Zohar Vayakhel 219: Since some evil beings are neutralized and bound, and the Other Side is bound, it cannot rule nor denounce. Therefore it is called an altar (mizbe'ach). When the Other Side saw the smoke of incense rising, he surrendered and fled, and could not approach the tabernacle, so it was purified. And no one delighted in that high joy but G‑d alone. Since He is very fond of it, the altar stands inside, for there are blessings in such an altar, and therefore it is not exposed.
...wherever the section of the incense is said with intention and a willing heart, death has no sway over that place...
It is written about Aaron, "And he stood between the dead and the living, and the plague was stayed" (Numbers 17:13). For he bound the Angel of Death, so he could not have power at all, nor carry out punishment. A sign was given to us, that wherever the section of the incense is said with intention and a willing heart, death has no sway over that place, nor can it harm. Also other nations have no power over that place.
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Come and see: whoever is pursued by Judgment, is in need of incense and must repent before his Master. For it helps judgment to disappear from him. And surely judgment leaves him, if he is wont to say twice a day, morning and evening, the passage of the incense, as is written: "sweet incense every morning... at evening, he shall burn incense upon it" (Ex. 30:7-8). Upon this, the world continually exists, as is said, "a continual incense before G‑d throughout your generations" (Ibid. 30:8). Assuredly, this world is sustained by it and so is the World to Come.

Wherever the section of incense formulation is not daily mentioned, judgment and many plagues hover above this place, and it is ruled by other nations. Therefore it is written: "a continual incense before G‑d." It stands always before Him, more than other devotions. The section of the incense is more precious and delightful to G‑d than all other worship and petitions. And though prayer is most valuable, the section of the incense formulation is highly regarded and precious to Him.

Come and see the difference between other prayer and the section of incense. Prayer was composed instead of the sacrifices offered by Israel. But all those sacrifices are not as valuable as the incense. Also, the difference between them is that prayer perfects whatever needs perfection. Incense, on the other hand, does more by both perfecting and binding, and brings more light than anything else, which removes filth and cleanses the tabernacle. And everything is shining, perfected and joined together.

Therefore the section of incense is recited before the prayer every day, to remove filth from the world; for it perfects everything on that day, like a desired sacrifice with which G‑d is pleased.

...the section of the incense comes before prayer, hymns and praises. Come and see, the incense always comes first and precedes everything. For this reason the section of the incense comes before prayer, hymns and praises. For nothing rises, is perfected or connected, before filth is removed. It is written: "and he shall make atonement for the holy place" first, and then "because of their transgressions in all their sins" (Lev. 16:16). Therefore, one should atone for the holy place, and remove filth, and purify the holiness and then sing hymns and pray, as we already said.