When we speak about a black holes "Insides" and "Outsides" we usually mean inside and outside of the event horizon. The event horizon is the distance from the singularity to the point which nothing can escape the gravitational pull, not even light. The event horizon is also known as the Shwarzchild Radius which can be found as R=(2*G*m)/c^2. The strong gravitational field is able to affect everything that gets near , this introduces the phenomenoa known as gravitational lensing. Gravitational lensing is when the gravitational force causes light from behind the black hole to bend around the event horizon. Closer to the event horizon light can be bent in such a way it seems to "orbit" the black hole. If you were able to travel this path, the light would be bent so much you would be able to see the back of your own head!

Another well known phenomena is that fomation of the accretian disk around the black hole, the acrettian disc is the part of the black hole that can actually be seen by the naked eye. An accretian disk is a disk of matter usually pulled from wandering stars that builds up around the black hole. The accretian disk is usually a 2-D disc, the direction of it is usually decided by the spin of the black hole itself.

Event horizon of a singularity (left) [5]                                          Interpritation of accretion disc buildup [6]