What is this line when I snap two corners together?

@wrongwright, the button to the right on the snapping settings is ‘Align Rotation to Target’.
Turn that off and the line will not show.

Align Rotation to target can be used for snapping objects such as screws to align with the target objects face/edge/vertex. Instead of trying to manually rotate the the screw in to the correct position.

When snapping vertices there is not much point to it, you can turn it off or just ignore it.

In other words, it’s nothing to worry about, it’s just a visualization that 99.9999% of the time you wont use or wont have to pay any attention to. I see it as a way to make me look cool, when I’m using Blender and there’s people around and I snap an object and a line shows and it looks complicated and people are like wow that looks so complicated, you must be a genius knowing all this stuff, I’m like yeah.