"The Altar": not "an altar," or "that altar," or "this altar," but the altar. Okay, well we know the poem is about an altar, and even if we weren't sure, it's arranged in the shape of neat little altar so we would probably figure it out eventually, right? Right. So what's why the word "the" anyway?
First, if you've read our "In a Nutshell" section, you know that the poem was published in a little volume called The Temple (1633), and that each of the three sections was named after something to do with a church ("The Church Porch," "The Church," and "The Church Militant"). Well, "The Altar" is the first poem in the "The Church," and it is called "The Altar" because, if you imagine the speaker giving you a tour of his book-temple-church, then you can imagine him saying, "here is the altar folks."
Okay, so far so good. If the poem is the altar in Herbert's poetic church, what else does this mean? Well, if the altar is a special table used in religious ceremonies (prayer, praise, readings, and the like), it follows that it is also perhaps one of the most important items in the church. It's kind of like a centerpiece, the basis for just about everything that happens in church.
The poem itself is the basis for all the other poems in the second section of "The Temple," but it also describes the basic elements of praising, sacrificing, and worshiping God. The altar of religious faith, you could say, is the painful labor of offering one's heart to God (that's where all that business about building an altar out of one's heart and cementing it with tears comes in), which is just what our speaker is describing in the poem.