There are currently over 50 different plane types and your goal is to unlock them all while also earning coins in the process. Each plane you unlock will give you double the coins of the previous one.
At the outset of the game you can either add the base level aircraft to your hanger by purchasing them or alternately just be patient and wait for the boxes with them inside to appear for free. For this to happen though you must be actively playing the game. Every so often a video offer will appear that will allow you to upgrade one plane for free in return for watching an advertisement. Also, when you sign in after being away for a while watching a video advertisement when one is presented to you will allow you to double your offline earnings.
Upon reaching the level 5 plane you will be able to unlock increasingly advanced aircraft to purchase from the store with coins as well as gems. Also from this point each new plane that you unlock will allow you to buy one plane up from the previous highest-level plane in the store. This enables you to use the coins you earn to further upgrade your planes and move things along.