What do we mean when we say it today?
No offense to the little guys from Turbo, but we don't think snails actually go that fast (unless they're animated by Dreamworks of course). In reality, snails are pretty darn slow.
All this phrase means now is that someone or something is moving reaallllly slowly. It's taking way longer than it should, so it gets slapped with this label. To be fair, when people are really slow, it gets irritating, especially if you're in line behind someone who is moving a snail-pace, because we can go faster than itty-bitty bugs.