Cliff was the second oldest of the Tannen Brothers. In this alternate reality, their father Irving "Kid" Tannen never went to prison, allowing him and the Tannen family to reign supreme as a criminal syndicate for over fifty years in Hill Valley.
Behind the scenes
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.
No real information about Cliff's personality are expressed, save for the Tannen family disposition towards meanness. He couldn't have been born any earlier than 1938, even if he was conceived directly after Biff's birth.
Cliff Tannen was voiced by Andrew Chaikin.