This term is specific to Tribes Vengeance. It refers to using the Grappler (a weapon that lets you attach yourself to walls and ceilings and winch yourself towards the grappled item or even swing from it) to swing around an object in a circular motion to avoid being hit by enemy fire. Named after the first player to have risen in complaint over the technique - whose nickname is "Bodom", obviously a reference to the Lake Bodom murders - the act of "Bodoming" has drawn the ire of many.
It looks hilarious. Picture a guy wearing futuristic power armor and a jetpack flying around in circles on the ceiling like a tethered model airplane!
John: Look at that Bodoming fucktard up there! He's ruining the game for everyone!
Brad (Using the game's built-in character animation "emote" system, during which his character says a pre-recorded line and then swings his arms and legs around like a limp-wristed homo): Dance, little friend!
John: You guys are a worthless excuse for a team. I'm leaving.