You have 5 gifts to send to your friends. If the gift counter is zero, you must wait 23 hours to get 5 new ones.
When the gift counter resets, you can send gifts to the same friends again.
You can have only 20 gifts in your inbox (Messages tab) at the same time. If you have more than 20 messages it means all the other ones are Friend Invites.
The gift can contain one of these objects, created in a blazing bubble with the text Friend Gift: