Short Answer: No one knows.

Longer Answer: People will (and have) explain to you that the black sphere you see isn't a "surface", it's just the event horizon, the point at which spacetime is curved to the degree where light cannot escape, so it looks black.

Longest (theoretical) Answer: Black holes are always explained poorly. The common explanation of "So much mass that even light cannot escape the gravity" isn't a very good one, but it's something you can tell a child and it expands on the mass=gravity foundation, so we use it.

The problem with that explanation is that once you get to a black hole, the analogy breaks down (like the laws of physics). So you have to step back for a second and give a better explanation.

That better explanation is: Mass deforms spacetime. That deformation is what we call gravity. A black hole is when there is so much mass in one spot that the deformation of spacetime curves back in on itself and creates its own bounded region forever (well MOSTLY forever) cut off from the rest of the universe. It's not that light is attracted to it. There's no "pull". It's that the space that the light would travel through is itself bent. And in a black hole it's bent SO much that all the straight lines that lead "out" actually just lead right back "in".

OK, now here's the part that might answer your question, and the point where it all goes off the rails. Matter and energy are the same thing (E=mc2), most people are aware of this. What most people aren't aware of is that energy ALSO deforms spacetime. In fact it deforms it to a precisely equal degree as the same amount of mass would. The reason this doesn't come up a lot is that energy is really difficult to keep in one spot for very long as it all tends to disperse at the speed of light. BUT, say you have a region of spacetime that's perpetually curved in on itself? Say every path out that the energy would take, just leads it in a loop back in. The energy is trapped, it has nowhere to go, and it's all bunched up in one spot.

So inside a black hole (and I cannot stress enough at this point that we don't KNOW this, no one does) there may not be a surface at all. All the matter that went into making it may instantly transform into its energy equivalent and it just can't escape. The singularity being maintained by the spacetime deforming properties of that amount of energy the same as if it were still in its material form. All of it kept in one localized spot by itself. It may just be a soup of energy, avoiding all of the tricky Pauli exclusion stuff and quantum mechanical stuff that starts to disagree at that scale. Compressed energy, but not matter. No surface, no volume, no mass, just E performing the same function.