The Pump shotgun is close combat weapon mostly useful early to mid-game due to the fact that it has a relatively good damage output and a decent firing rate, but its main drawback is that it has a limited range (as typical with a shotgun). As a result of its attributes, the Pump shotgun is generally a solid option for close-range combat throughout the game, but more-so in the early-to-mid game; there are generally better options for close-quarters weapons in the late game however, as weapons such as the Charge rifle become more common. Due to the short range, decent weapon accuracy, and fast warmup & cooldown times; the Pump shotgun is a great weapon for those with perhaps lower shooting skill, as they'll still be somewhat useful in close-range engagements - and this makes the Pump shotgun a decent counter against Tribals (particularly those with pila), partially due to their complete lack of body armour.
It's a somewhat common weapon (in the early-to-mid game) used by Pirates and Outlanders. If you have weapons with medium-to-long range at your disposal; these raiders are usually out-ranged and may be shot down before they even get a chance to fire.
When this weapon is used at close range and lands a successful hit, the effects can be devastating: It's easily capable of killing or incapacitating most enemies within a couple or few successful hits. Because of this and its reasonably high damage per shot, it's not rare to destroy body parts or organs. It will more likely severely damage body parts and organs, making this a less suitable weapon in some respects for obtaining useful prisoners.
The Pump shotgun seems to have the appearence of a variant of the Rimington 870.