An open vent on a window air conditioner allows fresh air from outside to come into the home and circulate along with the cool air produced by the unit. A closed vent prevents warm, fresh air from entering the home.
While an open vent is not ideal for efficiency, since the unit has to work harder to cool down the warm air, it does serve a purpose. Leaving the vent open refreshes stale air and removes odors from the room. Additionally, the vent makes it possible to run the unit on the fan-only setting, which simply pulls in air from outdoors on cool or mild days.