This should help explain it for you.
Because I keep all my zip files in a separate folder, I do keep the edr files.
Hint: More people would have seen this post if you had placed it in the Embroidery section of Community instead of the Chat sect
I don't keep them!! Here is an explanation that I found..
The EDR file type is primarily associated with 'Embird Plus' by Embird. Embroidery design software. The EDR file contains the color palette for Embird Plus (colors are stored in this file when displaying embroidery designs).