A barrel roll occurred when an object (such as an airplane or starship) made a complete rotation on its longitudinal axis while following a helical path, approximately maintaining its original direction.
When a cascade virus disabled the USS Defiant's computer systems in 2373, which included the stabilizing gyros, Chief O'Brien warned against making sharp turns lest Captain Sisko wanted to do barrel rolls. Jadzia Dax then quipped, "that could be fun". (DS9: "For the Uniform")