A Garden of Eden pattern in John Conway's Game of Life is a pattern which is not the successor generation of any other pattern.
Some patterns are the successor generation of many other different patterns. For example, a 'pattern' with all dead cells is the successor of a pattern consisting of one live cell; the same pattern is the successor of a pattern consisting of two live cells. This pattern:
is the successor generation of itself, and it is also the successor generation of this pattern:
Garden of Eden patterns, however, are patterns such that no pattern will generate them. There is no previous state which will become a Garden of Eden pattern (ever). The name is a very appropriate one - it suggests that the patterns are 'supernatural', the result of a Creator which does not have to work within the Laws of Physics.
One Garden of Eden pattern is the following:
Glossary.doc, A Brief Illustrated Glossary of Terms in Conway's Game of Life, compiled by Al Hensel, and some example files found on the Web.