Pokemon; Pallet's New Heroes
Badges are just that. Badges. More specifically, they are symbolic of a trainer’s victory over a gym leader. Once a trainer has completed the full set for a region, they may join that region’s tournament.
Of course, many trainers have no interest in the tournament and take the veiw of “Badges? Badges?!? We don’ need no steenking badges.”
They can be anything from lumps of rock to incredibly ornate jewels.