In Cosmology, horizon crossing refers to a class of processes whereby boundaries are crossed, which often coincide with a point of no return. For example, Black Holes are surrounded by an event horizon. Once an object, an astronaut or even a particle of light, crosses this horizon it may never come back. Our entire universe has a horizon. In this case, it is a causal horizon. Only objects that are within our horizon have a chance to interact with us.
Horizons in Theoretical Physics are clear demarcation lines, but there is nothing peculiar about this border in a Black Hole. If you were to cross it, you would not be able to realize it directly – space-time is locally as flat as in interstellar space.