The Radio Room is a special room that help increase the happiness of your dwellers and also allow you to call in new dwellers from the wasteland. The Radio Room periodically sends out a signal. If no dweller heeds the signal, the cycle starts again. Placing dwellers with high Charm stat, merging, and upgrading radio rooms increases the chances of finding a dweller and greatly speeds up the signal cycle.
Radio Room broadcasts also attract Deathclaws. That said, consider building/upgrading radio rooms once you have fully equipped your dwellers to fend off the possibility of a deathclaw attack. You can have up to 10 dwellers waiting outside the vault entrance. Unless you let some of them in, you won't be able to call in new dwellers even if the radio broadcast managed to attract new dwellers.