Festival races are the main races in Horizon and will be indicated on you map with a coloured outline corresponding to the minimum wristband level you need to enter them. Each has certain class/model/drive setup restrictions to enter. Once you have an event highlighted on the map, drive to its location and enter it. You need to win the race for it to count, once you have won 10 races the achievement will unlock. This will likely unlock naturally as you progress through the game but to make it easier, set the AI difficulty to easy and turn on all assists.
NOTE: It seems this achievement is slightly glitched and doesn't count the first event even if you win it. If you placed first on the first event, this will unlock after winning your 11th race.