It's to simulate imperfect aim. In a game without bloom if you put the crosshairs on the center of a target and shoot it the game either hit scans or has bullet drop but it will hit the same spot over and over and over.
If a person were to shoot a real gun at a target they will "group" their shots around the target they actually aimed for. The bullets wouldn't all go through the same hole.
Everything from the rifling of the barrel to how you pull the trigger will cause a slight miss vs where you aimed. Even a very high skill shooter will only have a tight grouping rather than perfectly putting 30 bullets through the same hole.
Bloom is an attempt to simulate real shooting - each bullet will randomly miss the intended target by a small amount up/down/left/right randomly even if your aim is perfect.