What are the files?
*.mrimg files are typically backup files. One popular backup software, possibly the only one, that uses the file extension .mrimg is Macrium Reflect
Macrium Reflect can create an image of your hard drives. To restore the image you will need a copy of Macrium Reflect, which you can download over at www.macrium.com/reflectfree.aspx
Once you have it installed you can right-click on a *.mrimg file and select Restore from the context menu:
I already have Macrium installed – can I recover Mrimg files without booting up?
Yes, if you installed Macrium correctly there should be an additional boot options called Macrium Recovery or something similar.