Photons (which are the "particles" that make up light) have zero rest mass. To understand why photons "fall" into a black hole, you need to know a bit of general relativity. What general relativity says is that any massive object warps the spacetime around it. You can think of this with a simple analogy. Imagine a stretched rubber sheet that is completely flat. This represents the spacetime when there is no mass. Now, if you put a heavy ball in the rubber sheet, it will cause a distortion in the sheet. This is exactly what happens in space, except that it is in 3 dimensions instead of two.
Further, a photon always travels by the shortest distance between two points. As spacetime is warped, the light appears to bend around a massive object. In reality, it is not that the object is attracting light, but it is just that the photons are traveling by the shortest distance in a curved spacetime.
Around a black hole, the distortion of spacetime is extreme. At the event horizon of a black hole, the spacetime curves into itself and as a result, light cannot escape from a black hole.
This page was last updated June 27, 2015.