A fuse is a long distance block line, and where one block to be destroyed, all the blocks will be destroyed, but need to be timed correctly. This is useful in a small number of puzzles, most notably in Lighting The Fuse.
It doesn't actually matter how many points are at the intersection, or which direction it's going, which is a common misconception. As long as there are at least two cubes touching the one you're removing, and all chains going off are about the same length, it will light a fuse correctly. Otherwise, you only end up destroying the smaller or smallest segments branching off. This means that in the later game, when larger fuses are required, the Red Matter Gun is much easier to use.