Edit: So I asked this question last night on a whim, because I was curious, and I woke up to an astounding number of notifications, and an extra 5000 karma @___________@
I've tried to go through and read as many responses as I can, because holy shit this is so damn interesting, but I'm sure I'll miss a few.
Thank you to everyone who has come here with something to explain, ask, add, or correct. I feel like I've learned a lot about something I've always loved, but had trouble understanding because, hell, I ain't no physicist :)
Edit 2: To elaborate. Many are saying things like time is a constant and cannot slow, and while that might be true, for the layman, the question being truly asked is how does gravity have an affect on how time is perceived, and of course, all the shenanigans that come with such phenomena.
I would also like to say, as much as I, and others, appreciate the answers and discussion happening, keep in mind that the goal is to explain a concept simply, however possible, right? Getting into semantics about what kind of relativity something falls under, while interesting and even auxiliary, is somewhat superfluous in trying to grasp the simpler details. Of course, input is appreciated, but don't go too far out of your own way if you don't need to!