From Bulbapedia, the community-driven Pokémon encyclopedia.
The Big P Pokémon Race is a race held at the Laramie Big P Ranch in Safari Land. It is held to decide who has the best Pokémon that was raised at the ranch. The winner becomes an honorary member of the Laramie clan. The night before the race, a festival is held in Laramie Village. Although it is mainly entered by Trainers and one of their Pokémon, apparently Pokémon are allowed to enter as couples without a Trainer as well.
The race starts on a straight road. After this, an uphill climb over a steep hill follows. On the other side of the hill, the course goes down. The course continues over a set of rocks in a pond. The Pokémon either have to jump over the rocks or cross the pond over the water. Afterwards, the course goes downhill again, but this time there are plates of Pokémon food located on rocks to distract the Pokémon. Once the participants have passed this section, it's a straight road to the finish line.
In The Flame Pokémon-athon!, Ash and his friends met Lara Laramie, who told them about the race. Lara was going to enter, but at the festival she broke her arm. Seeing potential in Ash, she had him replace her at the race. Although Ash received strong competition from Dario, he managed to win.
Pokémon entered in the tournament