The radio station transmits a broadcast into the wasteland in order to attract new dwellers. Sometimes however, it may do nothing at all or even attract raiders and deathclaws. Its overall effectiveness is based on the assigned dwellers' charisma.
This room also helps raise happiness among vault dwellers. The happiness bonus appears to endure while a dweller is assigned to the room and is removed when once all dwellers have been unassigned. One update added the ability to toggle between broadcasting to the wasteland or just within the vault. This allows you to still get the happiness bonus without attracting new dwellers, raiders or deathclaws.