Every 24 hours you can send a gift to five friends. Open your Friends list to choose a friend you want to send a gift to, and then tap the Send button under their picture. If you've already sent that player a gift that day, the Send button will be replaced with a picture of a gift and a check mark.
Your friends can also send you gifts. If they do, you'll see a hot-air balloon with the sender's picture on it floating around your town. Tap the balloon to collect your gift and see the sender's name.
Gifts can contain coins, clovers you can use to play at the House of Luck, and Township Cash. During events you might also get temporary goods featured in the ongoing event.