I've heard that light can't escape from a black hole. Can it? If not, why?
I like to think of this in terms of escape velocity.
Escape velocity is the speed needed to escape the gravitational pull of a given object. For the Earth, that speed is 11.2 km/second (Mach 34!). When rockets blast off from Earth, they aren't trying to achieve a certain height or altitude, they're trying to reach a certain speed, the escape velocity.
Once a rocket reaches 11.2 kips*, it has attained the speed needed to leave the Earth completely. If a rocket fails to attain that speed, regardless of its height, it will fall back to the Earth. (You can imagine a magical balloon that slowly lifts you up into space, up past the ISS and most satellites, and then you let go: since you aren't going fast enough, you will fall back down, past all the satellites, and crash into the earth.)
Smaller gravitational bodies, like the moon, have smaller escape velocities. That's why the lunar landers were able to leave the moon with such a small ascent stage, compared to the massive Saturn V it took to leave Earth: they only had to go 2.4 km/second.
To escape the Sun, you'd have to go 617.5 km/second!
Fortunately for us, light goes faster than 617.5 kips, so we're able to see the light created on the Sun. However, as you increase the mass of an object, eventually the escape velocity would meet or exceed 299,792km/s, the speed of light. At that point not even light itself can go fast enough to escape the gravity well, and will always be pulled back down into the black hole.
*Short for "kilometers per second"
Don't forget that if a black hole has less than the current stable mass of a black hole (3 solar masses) then it evaporates - transforming its mass in radiation, in which case it would give off light, mostly X rays and gamma, at an increasing rate as its mass decreases, until the entire black hole is turned into a flash of hard radiation.
However, this light is the mass of the black hole escaping in the form of the most basic form of energy.
A black hole has an event horizon which 'marks the point of no return'. So yes, light cannot escape from a black hole.
Why? Well, think of a 'spacetime fabric'. It's the easiest way to understand the physics at work here, in my opinion.
Usually, the fabric would look like this:
However, a black hole has so much gravity that one could say it 'rips' the spacetime fabric:
When the light hits this area of amazingly intense gravity, it simply cannot get out - the light travels 'along' the fabric, and since there is a rip in the fabric, one could say it simply goes away - it becomes part of the singularity.
This is a simplification, of course, but it's enough to understand at least part of the physics behind this phenonenom.