Casual Mode (Newcomer Mode in the PAL version of Fire Emblem Awakening) is a play mode which was introduced in Fire Emblem: New Mystery of the Emblem and has been present in its successors.
The Fire Emblem series is known for its permanent death system. When a Player Unit's health reaches zero, they die (or permanently retire, depending on their importance to the story) and can no longer be used in any future battles unless revived via certain Staves or by restarting a level. Casual mode disables this feature, meaning that if a Player Unit's health reaches zero, they will retreat from the battle, keeping all experience and items gained during the map. They will be able to be used in the future after the chapter or battle ends.