In manufacturing and mechanical engineering, a groove was a long and narrow indentation built into a material, typically to allow an object to move within the groove and be guided by it.
In 2268, the Klingon Krell told the Neural native Apella that it was quite simple to cut grooves into gun barrels to make rifled barrels. Krell was going to show Apella how to do it inside a forge but Captain James T. Kirk and Doctor Leonard McCoy attacked them. (TOS: "A Private Little War")