A heterodiegetic narrator does not take part in the narrated action. S/he is therefore not a character of the story that is told. Very often a heterodiegetic narrator is omniscient (all knowing) or has at least a detailed overview of what is going on at any place of the story at any time. S/he usually has an insight into people’s thoughts and feelings as well.

A homodiegtic narrator is a character in the narrated world that s/he describes.

Both, heterodiegetic and homodiegetic narrators, can be either intradiegetic or extradiegetic.

Gray, Martin. A Dictionary of Literary Terms (York Handbooks). Longman, 1992.
Nünning, Ansgar and Vera. An Introduction to the Study of English and American Literature. Stuttgart: Klett, 2004.