Boarding (gameplay mechanic)
From Halopedia, the Halo wiki
Boarding a vehicle is a technique featured in Halo 2 and Halo 3. It is a unique and interesting way of removing the threat of an enemy vehicle while not destroying it so that the player may use it as their own.
If you can reboard a vehicle you have been kicked out of within ten seconds, you will earn the Maybe Next Time Buddy achievement.
Summary
Boarding, also called carjacking or hijacking, a vehicle is accomplished simply by holding X in Halo 2 or RB in Halo 3 (default controls) when the player is near an enemy's vehicle. This is not easily accomplished as the player can either be splattered or killed by the vehicle's gunner. However if the player succeeds he/she can instantly turn the tables on the enemy by using their former vehicle against them. But be warned, the enemy can do the same to you, so make sure you don't give them the opportunity.
In Multiplayer, a successful boarding of a ground vehicle will award the player the Hijacker Medal. If the player boards an aircraft the Skyjacker Medal is awarded instead.
In Halo 3, when ejecting an enemy driver the melee attack that takes place as you eject them severely damages the enemy and may even kill them if their shields are down. After being successfuly boarded, there is a brief period of time when you are stunned and cannot do anything. If you are being boarded it is impossible to get out and try to escape: you have to stay put until you are killed or ejected. This was not true in Halo 2.
Boarding Certain Vehicles
Ghost/Banshee/Chopper/Hornet
The most common kind of boarding takes place when a player successfully boards a Banshee, Ghost, Hornet, or Chopper. An animation will take place showing their character model jump on top of the enemy vehicle and eject the current driver. Then the player's character will enter the vehicle and the player will now be the driver. The Ghost and Chopper vehicles are the easiest to board because they only have forward firing guns so they're safe to approach from all other sides.
Warthog/Spectre/Prowler
Boarding a Warthog or Spectre is different in that you still eject the other player, but you do not enter his seat. This can be dangerous as the player that was boarded can start shooting you before you return to First-Person view. Because these vehicles also have a turret, it can be difficult to get close enough to board them, and because you cannot safely board a vehicle while there is an enemy in the turret. However if the player does get the opportunity he/she can render the vehicle useless by 1) ejecting the driver and thus the vehicle becomes a sitting target or 2) ejecting the gunner so that it is no longer a threat to other players (with the exception of the driver still being able to splatter people). Another funny way of boarding an enemy warthog is to get into the passenger seat and punch the rival spartan/elite driving, killing them. However, you may not want to do this in the middle of a battlefield however, seeing as you have to get out and run around to the drivers seat to take over the Warthog.
Scorpion/Wraith
When a tank is boarded, instead of the driver being ejected a different event takes place. The player can repeatedly press B to melee the hatch off the tank. After the driver is exposed you can either keep meleeing until the driver is killed or, by pressing the Left Trigger, plant a Grenade that will instantly kill the driver. However if you plant a grenade you may also destroy the tank in the process.
Mongoose
Halo 3's Mongoose cannot be boarded in the traditional sense of ejecting the driver or directly damaging him. However, a player may melee the driver off as you will still lunge like you would a ground enemy. Alternatively, you could get in the passenger seat of an enemy's Mongoose and then kill the driver with a few quick melee attacks or shots to the back of the head.
Counter-Boarding Tactics
A player can indisputably avoid being boarded simply by constantly moving at full speed sometimes even scoring some splatters along the way. However, if you are boarded by getting out of the vehicle before you are ejected, you may be able to re-board your captured vehicle. Additionally if you are boarded while inside a Banshee there is a maneuver that can be performed to recapture your stolen vehicle (The Great Banshee Switch).
If you are willing to sacrifice the vehicle, simply throw a Plasma Grenade right when you are boarded. It will destroy the vehicle and kill who ever hijacked you, works well as a last-minute kill in Slayer on Multiplayer but will ultimately result in your death as well, a costly sacrifice to the cause but you will get the kill, no matter what.
In Halo 3, if a Brute boards your Wraith, you cannot leave the vehicle to escape being beat to death. However, you can just fire the main cannon which will damage the Wraith but kill the Brute.
List of Characters able to Board
You are not the only one that can board vehicles. In Multiplayer or Campaign if you are not careful you may find your vehicle hijacked by these enemies: