"An airplane in flight"
Translation:비행 중인 비행기
Let's break it down:
비행 means flight, so that's easy to understand.
중인 is made up of two words. 중 means center/middle, and 이다 is the "to be" verb. The expression 중이다 is equivalent to "to be in the middle of", so when you say 비행중인, it means "to be in the middle of a flight".
비행기 means airplane. You can see that it comes from 비행 (flight), but the 기 itself doesn't tell you much. However, when you look at the word in Hanja (the Korean name for Chinese characters), you'll see that the 기 comes from the Chinese character 機, which means machine. So 비행기 literally means flying machine. You can see some other words that use this radical here, like 세탁기 (washing machine) and 복사기 (copying machine). Don't mistake it for the particle 기 that is used to transform verbs into nouns, that one doesn't come from any Chinese character.
Anyway, when you put everything together you get "a flying machine that is in the middle of a flight", or in human language "An airplane in flight".
비행기=airplane 비행=flight 중=middle or in the middle of doing something. Adding 인 to the end of 중 makes it an adjective. So it means "plane that is in the middle of flight".