REX is short for Revolver for Export, but as there was not heavy demand for it, it was never made available worldwide. This was primarily due to the break-action style, which is known to be structurally weaker than the modern and stronger swing-out cylinder style.
In Battlefield 3 it is the first weapon unlocked from the Co-op mode, It is also worth noting that its appearance in this game is one of the few times that the auto-ejecting feature is actually shown in reloading animations.
Battlefield: Bad Company 2
In Battlefield: Bad Company 2 the MP412 REX is a weapon unlock that becomes available for all kits once the player has reached 'Rank 15: Staff Sergeant III'. The ingame info browser describes it as:
"A 6 round revolver revered for its close range edge and notable Magnum firepower. Its top break design is a throw back to old 6-shooters of the 'Wild West'."
Once 'Rank 15: Staff Sergeant III' has been achieved by the player they are able to equip the weapon in their side arm slot.
In Brink, it is known as the "Caesar Revolver", following the game's trend of renaming actual guns to fictional alternatives. It was primarily a Pre-order only DLC item.