Some quarters spend a long time in laundromats or other coin operated machinery (used to be casinos too, before the advent of players cards... like a debit card)...
Anyway, the edges get worn down from all the coin chute travel. There's also what's known as a "dryer coin"... a coin that stays tumbling in a clothes dryer for many cycles to wear the edges down.
In either case, the faces of the coin will look beat as well.
As an aside... there was several years back a newspaper article about a batch of counterfeit Canadian coins making their way in Ontario. They were beat up looking, smoothed edged quarters, which upon further inspection would cost too much to produce as a typical counterfeit... later on, as the real powers that be further examined the suspect coins, the verdict... real worn out coins... probably from Winnipeg casinos!