The debrief buddy system is a way to make sure all players have an opportunity to deal with bleed and the after-effects of a game on a longer time-scale. It is simply that before the game each player is required to pair up with another player that they trust and promise to keep in touch afterwards with the intent to discuss any experiences or feelings that crop up later.
The benefits of a debrief buddy are manifold: Some after-effects will not show themselves until weeks after a game and can be very hard to deal with effectively, as can persistent effects that take a long time to work out. It is also a way to make sure no player is left entirely alone with their experiences. Some players will also not consciously realize that they need to talk the experience over, unless pushed to do so. It is also better for dealing with more complicated issues than a time-limited debriefing session.
Debrief buddies should keep in touch with regular intervals after the game, both checking up on each other and having longer talks as needed.
A good idea is to make it clear to players that if their debrief buddy is not available for follow up, they should contact the organizers as this may be a sign that their buddy is not coping well, since most players are eager to share their experiences or at least keep up the debrief buddy contract.