Healers have Recovery type Brave Bursts meaning they can heal your squad when they use their Brave Bursts. They can help a lot to get you through quests and minimize your use of Cure items.
You can get healers from the Rare Summon Gate such as:
You can get healers from quests and the Honor Summon Gate such as:
Do you want the cute goddess Tilith healing for your squad? Be sure to participate in Frontier Hunter events and you can acquire her at FH Rank 21!
Note that if you feel that your healer is too weak to survive attacks, you can have your healer Guard by holding down on the healer and swiping down. This will greatly reduce the damage your healer takes so that they can survive until you need to use their healing Brave Burst.
To learn more about the Honor Summon Gate please read the Honor Summon Gate article.