A phoenix is a pattern in John Conway's Game of Life in which every live cell dies every generation, but which survives as a whole. One example phoenix is the period-2 pattern:

...O....
...O.O..
.O......
......OO
OO......
......O.
..O.O...
....O...
which alternates with the pattern:
....O...
..O.O...
......O.
OO......
......OO
.O......
...O.O..
...O....
(which can be considered either a reflection through a vertical 'mirror', or a reflection through a horizontal 'mirror'). This structure will survive indefinitely (provided there are no other cells in the neighbourhood which disrupt the cycle), though no individual cell survives but a moment after its birth. Another way of thinking of a phoenix is this: it is a pattern which lasts forever using the standard 'rule' of life "23/3" (survival if 2 or 3 neighbours, birth if 3 neighbours) and produces exactly the same patterns for the rule "/3" (cells never survive, birth if 3 neighbours). The collective name for these patterns (there is more than just this one) comes from the mythical phoenix, which died to give birth to its offspring.

Source: Glossary.doc, A Brief Illustrated Glossary of Terms in Conway's Game of Life, compiled by Al Hensel.