When you replay a dungeon that you've already completed at least once, the Auto Play option will be available. Auto Play is also available in event dungeons and Titan battles. To activate or deactivate Auto Play, tap the Auto Play button.
Auto Play will draw cards up to 15 and then attack. Auto Play will also automatically use skills when they are fully charged, except the card manipulations skills that affect your hand of cards. You will have to use card manipulation skills manually. Auto Play automatically targets the leftmost enemy of the room.
Remember, Auto Play is not quite as smart as you, so you should only use it in easy dungeons!