The story
From quarter + staff, attested since about 1550. Probably originally referred to a staff cut from the heartwood of a certain size of tree which was cleft into four parts, per the OED.
Etymology from Wiktionary, CC BY-SA 4.0.
quarterstaff
Today it means: A wooden staff with an approximate length between 2 and 2.5 meters, sometimes tipped with iron, used as a weapon in rural England during the Early Modern period. Full definition →