The first altar mentioned in the Word was the one built by Noah after he came out of the ark, after being saved from the great flood. On that altar, he sacrificed clean animals to the Lord.

Mountains represent the Lord because of their height; we need to raise our thoughts above worldly things when "talking" with the Lord. An altar is a small artificial mountain. When it's used in worship, it can call to mind this raising of thought. The fire and smoke that rise from an altar are symbolically being sent to the Lord.

Most altars were made from unhewn stones. Stones represent truths. Unhewn stones - ones that have not been shaped by men - represent truths from the Word, truths that have not been adulterated.

The clean beasts to be sacrificed represent good things, charitable acts done because they are right. The clean birds represent thoughts about doctrine and actions, and about what is right. Presenting these things is an acknowledgment that we have them from the Lord, and a giving thanks to Him for them.

In the Israelitish Tabernacle, the altar of burnt offering represented the acknowledgment of good and the altar of incense that of truth. For this reason this larger altar, which was outside by the door, was made of brass which signifies natural good, while the altar of incense was made of gold, which signifies love to the Lord from whom comes truth.

197. This is why places and spaces in the Word (and everything that involves space) mean matters that involve state - distances, for instance, and nearness and remoteness, paths, journeys, emigrations, miles, stadia, plains, fields, gardens, cities, streets, motion, various kinds of measurement, length, breadth, height, and depth, and countless other things - for so many things that enter our thought from our world derive something from space and time.

[2] I should like only to highlight what length, breadth, and height mean in the Word. In this world we call something long and broad if it is long and broad spatially, and the same holds true for "high." In heaven, though, where thinking does not involve space, people understand length as a state of good and breadth as a state of truth, while height is their difference in regard to level (discussed above in 38). The reason these three dimensions are understood in this way is that length in heaven is from east to west, which is where people live who are in the good of love. Breadth in heaven is from south to north, where people live who are in truth because of what is good (see above, 148); and height in heaven applies to both in regard to their level. This is why qualities of this sort are meant in the Word by length and breadth and height as in Ezekiel 40-48, where the measurements are given of the new temple and the new earth, with its courts, rooms, doors, gates, windows, and surroundings, referring to the new church and the good and true things that are in it. So too all the measurements elsewhere.

[3] The New Jerusalem is similarly described in Revelation, as follows:

The city was laid out foursquare, its length the same as its breadth; and [the angel] measured the city with the reed at twelve thousand stadia; the length and breadth and height were equal. (Revelation 21:16)

Here the New Jerusalem means a new church, so its measurements mean attributes of that church, length referring to the good of its love, breadth to the truth that derives from that good, and height to both the good and the true in respect to their level. Twelve thousand stadia means everything good and true taken together. Otherwise, what would be the point of having its height be twelve thousand stadia like its length and its breadth?

We can see in David that breadth in the Word means truth:

Jehovah, you have not left me in the grasp of my enemy's hand; you have made my feet stand in a broad place. (Psalms 31:8)

I called on Jah from my constraint; he answered me in a broad place. (Psalms 118:5)

There are other passages as well; for example, Isaiah 8:8 and Habakkuk 1:6. It also holds true elsewhere.