There are specific meanings for each achievement. For example, if you have flown 5 different airbus aircraft's you will receive an "Airbus" achievement. Below you will find some screenshots on how to check your achievements.
Also, there are different types of levels. As you can see, there is a number below the icons. For example, airplanes with 3 digits mean you are at the 3rd level (every 5 different airplanes flow - you reach a new level).
Go to your Profile → Tap on "Achievements".
Just tap on any achievement to see what is the achievement for.
The number below the icon means a type of level you've reached.
When you tap on the achievement, you will see the definition of it.