In this world, you can have any animal you find as a pet (and by any animal I mean anything) You just need to have a packet of MicroCubes in hand to catch the animal and make it your own pet, or MicroMon. In turn, your MicroMon will do many things for you, depending on its abilities. For example, if you catch Razer, the steel MicroMon, he'll mow the lawn for you.
Of course, you are supposed to catch MicroMon for one single purpose: MicroMon Duels.
MicroMon Trainers are specially educated to command the right attack of the right MicroMon in the right moment (more about MicroMon Trainers later) They are the ones that determine the fact that not only the strongest MicroMon wins a battle.
One important thing to have in your mind while battling is the MicroMon Chart, which determines the forces of any element against another one. You may recall logical ones: Water beats Fire, Fire beats Ice. BUT there are many other types of elements. Here's the complete chart, with > meaning "beats", <> there might be a dispute):
Water > Fire > Ice > Steel > Electricity > Flight > Occult <> Darkness <>Light
(See if you understand it...)
MicroMon come in assorted sizes and with many features.