Time can be warped, as it is part of the space time continuum, but this only affects our passage in time relative to others - ie, you're moving as normal for you, but in a way that is different compared to somebody outside of the distortion.
It all come back to light cones. At any event, because light speed is the limit to the rate at which any causal chain can progress, a hypothetical light cone moves outwards, which is the distance encompassed by light moving out from the event over time.
Now, because light is a wave, it accords to s=fw, or wavespeed = frequency x wavelength. Because it is energy, it is determined by e=mc² and e=fh, or energy = mass x speed of light² and energy = frequency x the Plank constant. So, because light is energy, it has mass: its energy divided by c². Gravity acts on this mass, so for the light to continue it has to do work, or expend energy to resist the gravitational pull. e is reduced, so, in accordance with e=fh, its freqency is reduced (because h is a constant). So, to go back to the start , because f is reduced, s, which is in this case c, the speed of light, is also reduced (w isn't increased instead for a reason I've forgotten).
Now, the speed of light in a vacuum remains constant to any observer, so this can't happen. Another more familiar equation comes into play: s=d/t, or speed equals distance divided by time. As s is reduced, time is increased, or stretched to you and I to maintain the relative constancy of the speed of light. So all the gravity actually does to light is bend it, so the light cones bend to - and dear god this is the worst explained exposition ever written by anyone ever, isn't it?
And I'm only embroiling myself in it because I can't answer a single question on my physics homework sheet.
EDIT - I just found this in a sketch book of mine, written when I was a couple of years younger and all of this was a lot fresher in my mind:
Speed of light is reduced when moving from massive body [for reasons decribed above]. This means that the light cone appears to have moved backwards, ie, a longer time appears to have passed since the event, so time has effectively slowed. So something situated in a weaker gravitational field has had longer time relative to something situated in a stronger one, so it has experienced a longer passage of time.