Like all Mainstream Pokemon Games, players can connect with other players in order to do a variety of things. However, since Pokemon FireRed was created in the days of no Wi-Fi, you must do so wirelessly with the Wireless Adapter. With it, you will be able to connect with other players in the Union Room accessible on the top floor of any Pokemon Center within the game.
Once in the Union Room, you will be able to see all the other players you are connecting to wirelessly. Of course, said players will need to be in close proximity to you in order to do so. In the Union Room, you can Battle and Trade Pokemon with these other players, as well as team up to crush berries. Though plenty of things to do, the Union Room was really just created in order for players to trade for the Pokemon not found within their game in order to complete the National Pokedex.