Black holes are black because as has been mentioned previously light cannot escape from within the event horizon.
In general relativity light always follows a straight path through space which is referred to as a geodesic. However around massive objects where space is curved, it no longer behaves as a Euclidian geometry. This means to an observer assuming a Euclidian space, the light appears to curve in presence of massive objects.
In a black hole the curvature becomes so great that the light cannot move outwards from the region inside the event horizon any more, hence making the black hole "black".
The escape velocity at the event horizon can actually be derived using classical Newtonian gravity even for light. Escape velocity is calculated from
It becomes quite clear that the mass of the smaller object cancels out and that the final escape velocity
only depends on the Mass of the large object and the distance from its center. If you want to find the Schwarzschild radius of a black hole of mass M, then you simply set the escape velocity = c and rearrange for r (really this equation should not be used for black holes but if you are new to physics it is a basic approximation).
The effect that the time seems to stop when something reaches the event horizon is linked to this effect of the photon not being able to escape the potential well around the black hole. If the light is regarded as a wave traveling away from the black hole, it is gravitationally red shifted, which through the invariance of c makes the time appear to slow down for the object in the proximity of the black hole. As soon as the object passes the event horizon, light coming from it becomes infinitely red shifted making it look like time stops to an outside observer. At the same time, through the red shift, the photons lose all there energy and hence technically have not escaped from the black hole.