Welfarism is the belief that humans have the right to use animals as we see fit as long as they are treated humanely. There may be some uses where the benefit to humans is recognized as trivial compared to the amount of animal suffering, such as dogfighting or fur, where the use is believed to be unjustified.
The term "welfarist," as an adjective, is used pejoratively by animal rights advocates to refer to a situation where animals will continue to be used with very minimal improvements in the care, confinement or slaughter of the animals.
The term "welfarist" is also used as a noun to describe a person or organization who supports welfarism. Again, the term is sometimes used derogatorily by animal rights activists to describe someone who purports to be animal advocate but ultimately supports welfarism.
Animal welfare is different from animal rights. The animal rights position is that humans do not have a right to use and exploit animals for our own purposes, regardless of how well the animals are treated.