In archery, a Stabilizer is a counter-balance weight intended to help shooters keep a bow steady when shooting, as well as reducing hand shock, bow noise, and bow vibration. Stabilizers are made out of various materials, the most common found in modern bows being carbon and ABS plastic, and can be specially designed for either hunting or target shooting.
— In-game description
The Stabilizer is a weapon accessory exclusive to the Phantom in Battlefield 4. The attachment acts as counter balance for the bow, and allows it to be incredibly accurate when shot while aiming down sight. Similar to integrally suppressed weapons like the AS Val with its Suppressor, the Stabilizer is permanently attached to the Phantom and is the only attachment available in the accessory slot.
The Stabilizer in fact has no attachment entry in the game files and is actually modeled onto the Phantom, so its existence is primarily to justify the bow's high accuracy in-game.