On Gold's Role as a Champion of Ho-Oh
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A legendary pokémon usually chooses a champion when it finds a person whose moral code and beliefs match those of the legendary itself. If a person is seen as worthy to represent those ideals, they may gain said legendary's favour and receive its blessing for as long as they hold the title. A legendary can have several champions at a time, though it's rather unusual.
In Gold's case in particular, Ho-Oh chose him for his kind-hearted and honest nature, and the fact that even before acquiring the official League Champion title Gold would frequently go out of his way to help the people of Johto, mirroring Ho-Oh's role as a protector of the region. He continues to do so even after obtaining and abandoning the official League title.
Champions chosen by legendary pokémon are still only normal people. They don't gain superpowers or undergo any physical changes, but there are some minor perks to receiving a legendary's blessing. These effects may vary. Gold was blessed with slightly boosted luck, and things are generally more likely to go in his favour than is the case for other people. He's not aware of this.
Another perk of being chosen as a champion is that, as a result of the relatively close relationship between a legendary and its champion, the champion's prayers are more likely to be answered. Gold has the option to call upon Ho-Oh at any time and ask for its aid, though it is ultimately up to Ho-Oh whether he receives the help he asks for or not. Gold can summon Ho-Oh using the Clear Bell.
While there are no official duties or tasks associated with a champion role, the legendary pokémon can change its mind about a champion at any time and revoke its blessing if it deems them no longer worthy.