The Airport is used for changing countries in the game. You may want to change countries to race with your friends or if you would like to race your horse in a higher level country for more prize money.
When you change countries there are a few options presented to you:
Will show you where your friends are racing. Click on your friends name to go to the country they are racing in.
Will put you in the room with the least number of players.
Choose a country name from the list.