Badges have mystical and mysterious qualities that can somehow increase the power of the Pokémon owned by the Trainer who wields the badges; for example, the Boulder Badge increases the Pokémon's strength. In addition, badges that don't allow higher leveled Pokémon to obey, such as the Soul Badge, do indeed allow the wearer to control even legendary Pokémon such as Articuno.
It is not known what sort of material badges are made of, but it has been confirmed that the Gym Leaders each own a badge made of different material than the kind given out to normal trainers, as that is how the Masked Man's identity was narrowed down to among the 16 known Gym Leaders when Aibo scraped off a part of his hidden badge with its Scratch attack.
Badges are not required to enter the Pokémon League tournament; however, without eight badges corresponding to their home region, a Trainer must battle their way in to qualify for the finals.
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Cursed to silently watch; never again to live a youth's life.