You can do a whole bunch of stuff here, first of all, there is a gym here, which you can battle to get your 3rd badge, in Emerald, you can rebattle this gym after you beat the elite four. You can also get your first bike or you can switch bikes here. There is also the game corner here, which you can play at to win special TMs. Plus, you can get the HM Rock Smash here.
Here you are given your very own bike! You are given the option of taking the Acro Bike and the Mach Bike. The Acro bike is slower, but has better acceleration and is easier to turn. Your choice does not make a major difference, as you can exchange bikes at any time. However, each bike allows certain places to be accessible.
Mauville Game Corner
The Mauville Game corner has lots of TMs. This Game Corner has Psychic, Flamethrower, Ice Beam and Thunderbolt!
This is the only Game Corner in Pokémon Ruby and Sapphire. There is another Game Corner in Mossdeep City for Emerald users.
In order to play at the Game Corner, you first must acquire a Coin Case. Talk to the lady in the house beside the Poké Mart. She will mention Harbor Mail, which needs to be bought in Slateport City. If you didn't buy it or obtain it at the Trick House's second puzzle, you can take the bike route there and back. The Harbor Mail may be exchanged for the Coin Case.
The Game Corner has two games - slot machine (with a chance of a high payout), or roulette (which has a slow but steady payout.)
Mauville City Gym
This Gym specializes in Electric types. It is recommended that you bring a Rock Type Pokémon like Geodude which can be found in Granite Cave in Dewford Town.
Watson can be the first major challenge for many trainers. His Pokemon will electrocute Flying and Water types, and his Magnemite and Magneton will resist most forms of damage. To top things off, Voltorb is a powerful speedster, with Sonicboom and Selfdestruct threatening to deal relatively major damage.
A ground type Pokemon like Geodude will be immune to dangerous electric attacks, although it will still have worries thanks to the sheer power of Watson's attacks. If you picked Torchic to start with or have gotten yourself a Pokemon with Fighting moves, you will be glad to hear that Watson Magnemite and Magneton are weak against Fire and Electric attacks.