They want to know that there is a responsible human being (theoretically) at the premises who would be able to accept service of process or other official notifications.
A PO Box is just a box; U.S. Postal Service workers have no particular obligation to accept these notices on your behalf.
Because they do not want to disclose their home addresses, the owners of startup companies sometimes use corporate identity programs at places such as Regus or HQ Global Workplaces, or services such as "Mail Boxes Etc." or "UPS Store," since they offer street addresses and not a PO Box.