Media files are your pictures, music, videos, and documents.
If your phone accepts a micro SD card, these are the files you want to transfer to the card.
As @ManiacJoe said, pictures, music, videos, and documents. And you can uninstall any apps you've installed that you don't use. (Other than that, if you start deleting files, you could end up with a phone that doesn't work.)
The solution to "I need more space" is "buy a phone with more space". The amount of space you're given is a lot less than the advertised space. A lot of the space is being used by the phone itself. (For instance, there's a whole Linux installation in there - Android is a program that runs on Linux.)