Why can't light escape from black holes?
Nothing, not even light can escape a black hole if it gets too close. This is why they are called black holes. It is difficult to explain precisely without introducing some complicated ideas.
The simplest analogy is to consider throwing a ball up in the air: if you throw it fast enough it can escape off into space, but if not gravity will pull it back down to Earth. If we were to increase the gravity you would need to throw the ball faster and faster. Eventually there would come a point when you would have to throw the ball at the speed of light, which is the maximum speed anything can travel. At this point we have a black hole, and nothing will be able to escape. This is quite easy to understand, but has a number of flaws. For example, in this picture light would slow down, then stop, and then fall back towards a black hole: this isn't right, as light always travels at the speed of light.
A slightly more accurate but complicated picture is to think about gravity as the effect of the bending of space. In general relativity, which is our best theory of gravitation, mass bends space. This is often visualised as a rubber sheet being stretched by something heavy. Particles (whether light or matter) want to travel along straight lines, but when space is curved these become bent: they instead follow curving paths which we describe as the effect of gravity. Black holes have very high curvature, beyond a certain point (known as the event horizon), all straight lines are curved such that they point inwards towards the black hole. There is no direction you can go that will take you outside the event horizon! That might sound a little odd, but black holes are strange places. It's best to keep a safe distance.