At the very center of a black hole is the . . . middle. Beyond that, we really don't know. Black holes are incredibly new to science. While they have been theoretically possible for decades, it's only been in the last decade that astronomers have had sufficient evidence to confidently claim that black holes exist. They are so confident about it now that astronomers now believe that black holes are present at the center of every galaxy.
The problem with black holes is that they are black, and they are holes. Because they don't emit visible light, they are extremely hard to study. What we do know about black holes is that they are massive. Really massive. So massive that normal physics and math sort of falls apart when applied to black holes. Right now, the leading theory about black holes and their centers is that at the bottom and center of a black hole is the singularity. If something were to fall toward the singularity, it would quickly become crushed down (due to extreme gravity) to be the most dense thing in the universe. And now the weird part. It would be the most dense thing in the universe and take up zero space. Another way of putting it is like this: The singularity is the point that has infinite mass in an infinitely small space. Mind . . . blown.
There is no way for us to go even near a black hole yet, since they suck up all matter, so there is no way to know for sure what is in a black hole. However, there is a popular theory that the center of a black hole consists of all of the matter in a black hole piled up at one spot, which is called "singularity". This has been theorized through equations, yet there is no complete quantum theory for the black hole yet. So, to conclude, we don't really know what is at the center for sure.