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:
OO
OO
is the successor generation of itself, and it is also the successor generation of this pattern:
O.
OO
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:
OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO
OO.O.OOO.OOO.OO.O.O.O.O.O.O.O.O.O
O.O.OOO.OOO.OOOO.OOO.O.O.O.O.O.O.
OOOOO.OOO.OOO.OOOO.OOOOOOOOOOOOOO
O.O.OO.OOO.OOO.O.OOO.O.O.O.O.O.O.
OOOO.OOO.OOO.OOOOO.OO.O.O.O.O.O.O
.OO.OOO.OOO.OOO.O.O.OOOOOOOOOOOOO
OO.OO.OOO.OOO.OO.OOOO.O.O.O.O.O.O
OOOOOOOOOOOOOOOOOO.OOOOOOOOOOOOOO
Source: 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.