Makes the primary weapon burst-fire. There are 3 projectiles in each shot. It has no effect on weapons that already fire 3 shot bursts, like the ARX 160. Weapons that fire more than 3 shots per burst (Tavor) are less effective with it, because it descreases number of shots in the burst. It also decreases the amount of damage dealt to enemies by 35%. Strangely, despite the fact that it says that only the primary weapon is burst-fire, secondary weapons are also affected.
Anyway, Burst Modules are not recommended to be used on weapons with incredibly high fire rate or that are full-auto, like Machine guns and Elementals. You could use it to save ammo, but those weapons already have high ammo packs, and low DPS so it isn't worth.
Burst Module is best used on Sniper Rifles because they have low fire rate and mostly are not even semi auto...some weapons like Intervention that need to fire several shots to kill the enemy can kill them quickly, from one burst. It is also very helpful with Rail Gun and Fortune's 500.
You can also use it on Explosives to get effect similar to M202 (multiple rockets!) and GL06, to make sure your enemy does die with both grenades stuck to their body. The Burst Module is also excellent for Bam Bam, as AIs wielding Bam Bam with Burst Module attached can cause mass destruction to a crowd of enemies.
Burst Module is considered the best attachment by many people.