Why does light slow down in glass?

The short answer is that light doesn't slow down in glass; it bumps into more stuff and doesn't take the shortest path through all that matter. If you looked at each individual photon, they are still going at the speed of light. We don't see individual photons though; we see A LOT of photons together. Here's a short explanation with more detail. If you think this explanation is too easy, here's a more in depth explanation that talks about the differences between how classical physics and quantum physics view the same situation in different ways.