A horizon is any surface which demarcates events which can be seen from those which cannot be seen.
In the case of a black hole, it is that surface surround the region out of which light itself cannot escape. No signal or information from within the event horizon can reach the outside universe. For a nonrotating black hole, the horizon is located at the Schwarzschild radius, corresponding to
Rs = 2GM/c2
In cosmology, the horizon problem is the conflict between the observed high uniformity of the cosmic background radiation, and the fact that regions of the sky separated by an angular size of more than approximately one degree could not have been in causal contact at the time of recombination.