So my pm box is almost full.

The "move to folder" option doesn't give a folder to move them to.

Is my only option to delete or to download them?

So what does download to
xml
csv
text

do?

I guess it puts them on my computer?

 

Downloading COPIES them all into a file to store on your computer for later reference.
To free up space you must delete some.

 

those are different formats to save the files to. I save mine as HTML or CSV (common format for excel etc)