Cats are a species of small predatory carnivorous animals that were valued by humans before the Great War for their companionship and ability to hunt vermin, such as rodents, snakes, scorpions, and other household pests.
After the Great War, many cats in what used to be the United States were hunted for food because they were an easy prey. Although not as common as before the Great War, domestic cats still survive as witnessed in the Commonwealth. Domestic cats are something of a luxury item; Stacy noted that her late mother kept a close guard on their cat. A woman in Broken Hills also noted feeding their cat.
According to the Nursery design document, various cats were to make an appearance there. There would have been friendly domestic cats kept by humans, as well as wildcats, bobcats and panthers that were hostile to the player.
If you use the perk Animal Friend on a cat and attack or get caught stealing from a settlement, all settlers will attack the cat as though it is a threat, though it is not combat-enabled.
With the Wasteland Workshop add-on, a cat can be captured in any settlement via a cat cage. Once released, it will add 10 bonus happiness points to the settlement (as much as some tier 1-2 stores). A beta wave emitter is not necessary to tame them. Also unlike all other captures, cats captured this way are protected.
Fallout 4 is the first canon game in the series in which cats are seen alive. (Fallout Shelter being non-canon.)
Killed cats will usually have cat meat in their inventory.