When two players kill each other at the same time. Most likely caused by the weapons being delayed instant-kills, such as rocket launchers, but can more rarely happen with hitscan weapons (i.e. weapons with no projectile travel time) should the players fire at the EXACT same time. Environmental explosives (e.g. explosive barrels) or being in a heavily damaged vehicle (e.g. rocket launcher vs. car) can increase the likelihood.
In a duel or two-team match where the most kills wins, the trade kill results in no net gain of points since both teams earn a point. However, in the rare case where one more kill will result in victory, even a trade will result in the leading team getting the victory. Some game modes only provide score for kills on certain criteria (e.g. headshots), which will make a net zero-score trade kill harder, if not impossible, to get.
In Halo 3, I saw a dramatic trade kill. Two Choppers from different teams boosted into one another. Since Choppers can even destroy other Choppers with their ram attack, both Choppers blew up and the drivers died.