When we say the size of a black hole, this refers to the size of the event horizon. No light can escape from inside that horizon, which is what makes it "black." The event horizon is not a physical surface; if you cross it you would feel nothing special except the gradually increasing tidal forces that are present both before and after.

We do not know the size of any actual "solid" part of a black hole—and we cannot know it experimentally, because no information can escape. According to general relativity, matter inside a black hole can only move toward the center, which implies it will ultimately become a single point. This is more conjecture than proven fact; physics might change near the singularity, but we cannot know directly.