What are black holes?

A Black Hole is a region of space (not a solid body) into which matter has fallen (from dead star) and from which nothing, whether material objects or light itself, can escape (Moore, 1974).

What causes them to occur?

A black hole is formed when a dead star collapses into a white dwarf. It is then considered a neutron star as it continually shrinks in size, becoming trapped in its own gravitational pull. In the final stage it has completely consumed itself in its own gravity, essentially sucking in all particles, include light itself.

The following images and animations represent this process:

What happens to a star with a certain mass after it dies (burns all its energy).

http://www.eclipse.net/~cmmiller/BH/blkform.html

Actual image from the Hubble space telescope.

http://antwrp.gsfc.nasa.gov/apod/archivepix.html