Barney was a man who lived in Hill Valley. In 1992, he complained to sheriff Andy Taylor about the fact that the electricity was out all over town. The sheriff told him to relax, and stated that he'd type up a warrant for the arrest of Emmett Brown, who caused the brown-out, if the electricity were available to do so.
Behind the scenes
Barney and Sheriff Andy Taylor are an homage to Sheriff Andy Taylor and Deputy Barney Fife of the Andy Griffith Show. Barney is not shown on-screen, but his voice resembles that of Don Knotts, the actor who portrayed Barney Fife.