Players can choose to purchase an item from the SHOP button on their screen, and Gift that item to another player on their Friends list.
Not all items are giftable, and only items purchased with Crowns (not gold) can be gifted. Just look for the little gift icon when you're shopping, select an item and click on Gift.
This Gift giving feature is controlled through Parental Controls. Players over the age of 18 will be able to send Gifts to any other player on their Friends list. Players under the age of 18 will need to enable this feature through the Parental Controls on their account.