The fancy rat is a domesticated

Domestication

Domestication or taming is the process whereby a population of animals or plants, through a process of selection, becomes accustomed to human provision and control. In the Convention on Biological Diversity a domesticated species is defined as a 'species in which the evolutionary process has been...

 brown rat (Rattus norvegicus), which is the most common type of pet rat. The name fancy rat derives from the idea of animal fancy

Animal fancy

Animal fancy is a hobby involving the appreciation, promotion, or breeding of pet or domestic animals.Fancy may include ownership, showing, trialling and other competitions, breeding and judging. Hobbyists may simply collect specimens of the animal in appropriate enclosures, such as aquaria and...

 or the phrase "to fancy" (to like, or appreciate).

Fancy rats have their origins as the targets for blood sport

Blood sport

Bloodsport or blood sport is any sport or entertainment that involves violence against animals.Bloodsport includes coursing or beagling, combat sports such as cockfighting and dog fighting, or other activities...

 in 18th and 19th century Europe. Specially bred as pets since then, fancy rats now come in a wide variety of colours and coat types and there exists several rat fancy groups worldwide.