The term Bloom, or also know as Reticule Bloom, is very similar to the term Weapon Spread. They both relate to the loss of accuracy when firing, but the difference is where the inaccuracy is lost.
Weapon Spread, like this answer states, is where the bullet looses accuracy in relation to the distance of its target. A good example for this would be a Shotgun.
Reticule Bloom is where the loss of accuracy is center on the gun and is in relation to how fast the gun is being fired, and the target reticule becomes larger if not ceased.
Halopedia's definition for this is
reticle bloom, this is where sustained fire will decrease the accuracy of the weapon being fired and also increases the size of the reticle
Using a gif borrowed from giphy of the game Halo Reach, you can see the reticle become larger after continual, rapid shots making it more difficult to aim
