All of these words describe when two things are happening simultaneously (at the same time). Let's start with during and while.
Use during before a noun:
The people sitting in front of me were talking during the movie.
My boss seemed to be in a rush; she kept checking her watch during our meeting.
Use while before a subject + verb:
We'll buy the tickets while you wait in line for the popcorn.
The doorbell rang while I was taking a shower.
Sometimes, when the subject of the two actions is the same, we eliminate the second mention of the subject:
Emily broke her leg while she was playing soccer.
I like to listen to music while I'm exercising. or I like to listen to music while exercising.
We cannot do this when the subjects of the two actions are different:
I chopped the vegetables while my brother prepared the meat.
Two different subjects for the actions - "I" and "my brother"
Meanwhile is the same as while, but it is used only at the beginning of a sentence -and usually when there are two different subjects doing the two actions:
I was watching TV while my brother was studying. or I was watching TV. Meanwhile, my brother was studying.
In the meantime usually implies you are doing an action while waiting for something else to happen.
I will send you the text for the brochure tomorrow. In the meantime, you can start working on the graphics.
Chris will graduate from college next year. In the meantime, he's saving up money to buy a house.