The person who summoned them – Black Rabbit – explains that Little Garden exists solely around games which vary from life-and-death battles to simple things like card games. Miss Rabbit needs their help to save their community who have lost their ‘flag’ – the symbol representing their identity in this world. Without it, they are simply the ‘No-Names’. The trio agrees to help partly because they are all nice people, but mostly because they’re bored and think this task will be an impossibly difficult, utterly dangerous, filled with numerous pitfalls and evils, but also because they don't have anything better to do.
This is not Fullmetal Alchemist. You’re not supposed to be glued to the screen for 99% of what happens. Problem Children has an interesting enough storyline. You will be entertained and invested, but it’ll be more along the lines of ‘sit back and relax’ rather than ‘gripping and epic’. Don’t expect character development to be taken up to eleven and don’t expect Little Garden to be a well-explained, detailed environment. That is not going to happen.