Jaffees, according to ALF, were blood sucking leeches native to Melmac. They took the form of their host. Not much is known about jaffees. They overran Detroit (a city on Melmac), which became known as "jaffeetown." It is also known that jaffees are not vulnerable to boric acid, as Earth bugs are.
The name "jaffee" actually comes from the last name of one of the workers on the show.