It’s no surprise that the 木 in 棒 means “tree, wood.” But what about the tower of lines on the right?!
Henshall notes that 奉 means “to offer up.” In 棒 it means “to hold something in both hands.” The 奉 component also acts phonetically here to express “staff.” So we have a wooden staff held in both hands, which is to say a large pole or club.