A Double Beatdown is something that happens when two players have similarly low health and melee each other. Both players are killed and both are awarded the Beat Down medal.
This is something that has been a large cause of frustration among players, their cry being "Whoever shoots first should win the melee battle!" A Double Beatdown can also occur between two Gravity Hammer-wielding opponents or opponents with an Energy Sword and a Gravity Hammer attacking one another. However, a Sword-on-Sword duel in Halo 3 will result in a clash, not a Double Beatdown.
After the second title update (which added thirty new Achievements and made playlist changes, as well as adding new maps) it seems that Double Beatdowns occur less frequently, to a mixed reaction from the players.