There are 12 races in Gangstar Rio, involving cars, bikes, boats and jet skis. They vary in difficulty but you should be able to beat most of them without too much trouble. Some will involve you competing against AI players, while others will pit you against the clock. Finish the track within the time indicated to win.
Each race rewards you with an amount of R$, and this increases incrementally the more races you have done, eventually netting you 6,000R$ for the final race.
You can find details on the races, the rewards and any tips or notable points about them in the List of Races in this guide.