What does it mean if your betta looks like it has fur?

It has fur coat syndrome and will most likely not survive. If it is in an aquarium with other fish (especially fish related to bettas) you should get an antibiotic to treat the water with to prevent the other fish from catching it. It is normally caused by your bettas water getting to cold (below 74 degrees F). Bettas are tropical fish and like to have their water at around 78-80 degrees. Sorry about your betta.