Black holes come in 3 varieties: stellar (smallest), seed (medium sized), and super massive (found generally in the center of galaxies). Theoretically (according to General Relativity) they form from the collapse of a star from a super nova and can continue to grow from various forms of matter falling into it, forming a 'gravity well' At the heart of a BH, theoretically, is a 'singularity'(an infinitesimal point) of infinite density (as Ken pointed out) and spacetime curvature, surrounded by an 'event horizon' (kind of like an invisible shell around it). Once you cross that horizon you can never return to the universe from whence you came. Even light cannot escape from a black hole.

Space and time do funny things inside the black hole. They 'reverse' themselves (space becoming time and time becoming space) due to the nature of the extreme gravity and spacetime curvature. This feature is difficult to explain. Time slows down as you near a black hole, again a result of the extreme gravitational power.

There is so much more to tell about black holes, but the advanced mathematics are beyond my comprehension (and maybe yours too anyway) so this has been a thumbnail description at best. Black holes are probably the most mysterious entities in the known universe.