An idiom is an expression whose meaning cannot be directly derived from the meanings of the words it contains. Hence one of the meanings of the word “idiomatic” is “containing/being an idiom”, as in:
However, this is not the most common meaning of the word “idiomatic”. When English speakers speak about something being idiomatic, it means that it sounds natural. For example, trying to explain a difference between “wait for me” and “wait at me”, a native speaker could say:
In this context, the intended meaning is not that “wait for me” is an idiom (on the contrary, it is quite clear what it means). “Idiomatic” simply means “how a native speaker would say it”, and this is the most common sense in which this adjective is used.