The veil (paroket) that separates the Most Holy from the Holy Place organizes the tabernacle. Once this "firmament" is in place, the rest of the tabernacle gets itself organized - the ark on the west side of the veil, the table and the lampstand on the east (Exodus 26:31-35).
The screen (masak) that separates the court from the Holy Place has a similar effect. As soon as it's mentioned and described and "hung" in the text (Exodus 26:36-37), the court is ordered by the appearance of the bronze altar (Exodus 27:1-8). Once the heaven of the tent is set up, the earth of the court takes shape.
Like the other furniture of the tabernacle, the altar is made of acacia wood and overlaid with metal, bronze in this case (Exodus 27:1-2). The less-holy metal of the court is bronze, while the more-holy metal of the tent is gold. Holiness is linked with value, and with glory. The more glorious the environment, the more holy it is, the more expensive the metals used.
The altar is a square of 5 x 5 cubits, with a height of three cubits (Exodus 27:1). It's a shell with four walls (Exodus 27:8), not solid like the stone altars that are also found in the Bible and at archeological sites. At the top of the altar are horns (Exodus 27:2), one at each corner.
Inside the altar is a grating of bronze, which hangs from rings inside the altar, about halfway down the wall of the altar (Exodus 27:4-5). This is the altar used for burning animals; there's a gold altar in the Holy Place, but it's used only for incense. When a priest brings animal pieces to the bronze altar, he places them inside the altar, on the wood and fire that were on the grating.
When we piece this together, we can see a parallel between the altar and the triadic structure of the tabernacle. The altar is placed on the ground, and blood is sometimes poured out at the base of the altar (cf. Leviticus 4). Halfway up the altar, on the inside, is the grate. At the top are horns. Base-grating-horns correspond to court-holy place-most holy place.
That parallel helps us grasp what's happening in a sacrifice. Within the altar, on the grating (= Holy Place), the priest places wood and fire, as well as bread products and incense for the tribute offering (Leviticus 2). When he's done that, he's reproduced the features of the holy place within the altar. There's fire on the lamps in the Holy Place and there's fire in the altar; there's flour and oil made as bread on the table in the Holy Place, and flour and oil and bread in the altar; there's incense on the incense altar in the Holy Place, and there's incense in the altar.
Into that altar environment, the priest places the parts of a sacrificial animal. That represents the worshiper, or, better, the priest who acts on behalf of the worshiper. An animal entering the altar parallels the priest entering the tent to serve Yahweh on behalf of the worshiper. The altar is a portal into Yahweh's presence, allowing the worshiper to draw near through a representative animal.
The altar is a holy mountain within the tabernacle court. Sacrificial animals are like Moses, ascending into the fiery cloud of Yahweh's presence, and through the animal the worshiper also ascends.
The altar is also humaniform, like the tabernacle itself. Yahweh's food, His "bread," is placed into the "stomach" of the altar to be digested into smoke and fire. As the place where Yahweh's bread is served, the altar is also a table, Yahweh's table, where the priests serve as butlers and waiters.
Because the altar is a table, it is, as James Jordan has put it, a "communion site." The verb name altar, misbeach, contains the verb zavach, "sacrifice," which always connotes "slaughter for a meal." Animals are slaughtered near the altar (never on it), but the altar itself is the place where Yahweh shares a meal with His beloved Bride, a foretaste of a future marriage Supper.