Quarterstaves (plural), also known as a short staff or just staff, is a pole weapon. Used for stick fighting. Yep, it's a stick. So why call it a Quarterstaff? It it believed to be that they would cut a tree into quarters, and each quarter was shaped into a staff.
*Disclaimer: I have done extensive research on each of these weapons. I am aware that there are many different versions of each of these weapons. I am not trying to spread false information. If you know and can prove any information wrong, please let me know and I will fix my errors. I have at least three references for all research on the weapons I will discuss through the challenge.