The phrase "to be at loggerheads," in common parlance, usually means to be in a heated dispute. For example one might say, "Amy and Bob are at loggerheads over where to put the new couch." Looking into the origins of the term, if Amy and Bob were truly at loggerheads, it might be time to call the police.
In the old days of the U.S. and/or British Navy, back when the men were made of steel and the ships were made of wood, a loggerhead was a bar of iron or other metal that was heated until it was red hot. It was then stuck into a barrel of pitch to re-melt it for patching leaks and other uses. So you see, if two sailors were "at loggerheads," one had quite a fight on one's hands.