During is a preposition which is used before an activity to indicate that a parallel action is happening at the same time as that activity
- What did you discuss during dinner?
During is followed by a noun, which often represents an activity (During + noun)
- We had to call the doctor during the night.
Incorrect: She slept during watching the movie.
Correct: She slept during the movie.
While is a conjunction which is used to refer to a background period of time in which another activity happened
- They all took notes while the professor gave the lecture.
While is followed by a clause (While + subject + verb…)
- I met my wife while I was at university.
Incorrect: She ate while the movie.
Correct: She ate while she was watching the movie.