A black hole is a region of space with such high mass that nothing can escape, including electromagnetic radiation. General relativity's consequence that mass bends light suggests that enough mass within a small enough area could bend nearby light to the point where it cannot escape. Such an "object" could have a very small mass if sufficiently concentrated. The surface-shape delineating the volume from which light cannot escape is termed its event horizon.
Since black holes lose their ability to interact via EMR, they can be fully characterized from our point of view by their mass, rotation (angular momentum) and electric charge. The event horizon forms a sphere if the black hole has no rotation, and forms an ablated sphere according to the amount of rotation.
Three types of black holes are generally assumed to exist:
Stellar black holes are thought to form from stars that have burned off sufficient fuel their fusion no longer keeps them sufficiently hot to maintain the pressure to counteract gravity, allowing the mass to collapse (gravitational collapse).
Intermediate-mass black holes (IMBH, between stellar and supermassive, e.g., 100 to a million solar masses) have also been theorized and observations have suggested their presence.
A Planck hole is the smallest possible black hole according to quantum theory. It would be smaller than an atom but would have the mass of "a flea's egg", about 1/50000 grams. Hawking radiation, a theorized quantum phenomenon which might slowly dissolve black holes would instantly dissolve one that small.
Models for the formation of the largest black holes observed are a challenge, but there is no theoretical upper limit to the size of a black hole ignoring a means of forming it: conceivably the universe is a black hole in the process of formation, though current observations of the universe's expansion complicate such a theory.
Rotating black holes are more complicated, and virtually all black holes manufactured by astronomical events (e.g., core collapse supernovae) would rotate, at least a little. Models suggest a non-rotation black hole includes a point singularity (point where the equations governing normal space and mass reach zeros and infinities) at the center, but some models suggest a rotating black hole would have a disk-shaped singularity. Also, rotating black holes exhibit frame dragging, a rotation of space around them, and with sufficient black hole rotation, a layer of this dragged space can be traveling faster than light as compared to the surrounding space further out. This "faster than light" region is termed the ergosphere. (Such a region has been described as one in which a particle cannot stand still, and as far as I can understand, that's to say it is impossible for it to move fast enough, given the dragged frame it inhabits, to appear to be standing still in relation to the surrounding space further out.) The outer boundary of the ergosphere is termed the static limit or static surface.