Well...no one really knows what's going on, but I'll do my best to explain. We've all been brought here, for reasons unknown to us, and assigned Pokémon - which are the creatures you were referring to - as partners. As far as life here goes...we pretty much have the freedom to do whatever we'd like, but the general objective here is to travel to each city and challenge the gyms to earn badges. You're not required to do so if you don't want to, though; it's just a suggestion!

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Um, that's pretty much it... I hope I could help shine some light on the situation. If you have any more questions, I can try to answer them. I'm still fairly new myself so there's still a lot I don't know, but I think I can at least help with the basics.