There are a seven rooms between the trainer and Norman, excluding the entry and Leader rooms. These 7 rooms each come with a trainer, who specializes in a particular stat. For example - One room might be a Speed room. The trainer will most likely have fast Pokémon, and use X Speeds in-battle. On each door, there is a message announcing the specialty stat of the next trainer.
In the anime
The Petalburg Gym is the fifth Gym in the Hoenn region, with the leader being Norman, who specializes in Normal-type Pokémon. Ash visited Norman's Gym when he first started his journey through Hoenn, but did not challenge the gym until he acquired his first four badges.