Riff Tannen was a brother to Biff Tannen, along with Cliff Tannen, in an alternate 1986. He was part of the notorious Tannen family mob, the fifth largest in California. As his aged father, Irving "Kid" Tannen, was seen in 1986A, it is implied that because the elder Tannen was never convicted of his 1931 offenses. This gave him more of a free hand to father a family normally, whereas an imprisoned Kid Tannen found it difficult (but not impossible) to have sexual relationships with women, as in conjugal visits.
Riff wore a Fu Manchu and semi-long hair in a hairband, which during the late 1970s to the 1980s had been a popular style for men, particularly rockers. This combines with his name, given a guitar hook is known as a "riff".
Behind the scenes
No real information about Riff's personality are expressed, save for the Tannen family disposition towards meanness. He couldn't have been born any earlier than 1939, even if he was conceived directly after Cliff's birth. Since there have never been shown to be characters exclusive to only one particular timeline in any previous form of Back to the Future fiction, and that Biff has never been said outright to have been an only child, it is extremely likely Cliff still existed in the regular timeline as well. We simply never saw him and there was really no real point for Biff to bring his family up in a conversation during the movies. While only Biff was conceived during Kid Tannen's initial jailbreak, there's no reason to believe Biff's siblings couldn't have been conceived during conjugal visits, or later jailbreaks.
Marty's wondering about "When did Biff get brothers" stems from him never having any real reason to know Biff's immediate family background before then, not that they never existed.
Riff Tannen was voiced by Andrew Chaikin.