"Anchor block" is the term players use to denote the bottom left block of any game item/structure/entity. More technically, it's the the block that the game uses when determining an item's location. For layering purposes, the term is generally used in reference to items larger than the usual 1x1 block to denote the block over which no other block can be placed.
Ever seen a dungeon on the far right side of the world, such that half of the dungeon has been cut off? This happens because the random location of a dungeon is determined by its anchor block. You'll never see a dungeon cut off on the left side of the world or the bottom of the world, because the game will only assign a dungeon to an existing map coordinate. But the game doesn't keep track of where the rightmost block of any dungeon falls. So when a dungeon is cut off on the right, it means the game correctly assigned the dungeon's anchor block to an existing coordinate, but failed to account for the rest of the dungeon to the right of that anchor block in relation to the edge of the world.
In cases where the dungeon contains either a world machine (purifier, expiator, etc.) or an ecological crate, it appears that there's a failsafe that accounts for the anchor block of the machine or crate. However, it's possible to find worlds where half the machine or half the crate is cut off.
This also explains why sometimes you'll see a dungeon or bunker floating in the sky. If you look closely, you'll notice that such structures generate directly to the right of a sharply elevated land mass. The anchor block of the structure, however, is still in the background earth.
Understanding anchor blocks is crucial to getting the hang of layering items, since you can never place any block of one item directly on top of the anchor block of another item. In other words, you can never place a multi-block item such that any of its constituent blocks (be they anchor blocks or non-anchor blocks) overlap an already-placed anchor block.
You can, however, do the reverse: if you place a multi-block item, you can then place any part of another item on top of the non-anchor blocks of the first item. For example, if you start from the left and place a bunch of engines in a row going towards the right, you can easily overlap them. But if you start from the right and try to place a row of engines running to the left, it won't overlap. Similarly, if you start from the bottom and place a column of engines going up, they'll overlap. But if you start from the top and place a column of engines going down, they won't. This is because of the anchor block.
Short version: Given a placed anchor block, nothing (not even the less-tangible blocks of a multi-block item) can overlap it.
Exploder mechanics is another area that requires some understanding of anchor blocks. The important principle here is that the anchor block of the mob/player must be wholly above the anchor block of the exploder for the exploder to do damage. For more info on this, see the exploder page.