Staff means everyone who works at a particular place. You might suspect that the town library's not a very fun place to work if its staff is always incredibly cranky every time you visit.
Staff refers to all of the employees at a business, or especially a school, where the teachers as a group are called "the staff." A completely different meaning of staff is a long wooden stick or rod, particularly one that has a specific purpose — like a walking stick or a weapon. This is the original meaning of staff, from the Old English stæf. It wasn't until the nineteenth century that the word staff was used to mean "group of employees."