The MJR file is your installation key. It is used to install the license on your mac, and any other macs you want to use your license for MC on. You are allowed to use your license on any Macs which you, personally, own (within reason).
You need to open the MJR file with Media Center 20.app in your Applications folder. This will install the license.
This doesn't seem to always get registered correctly. You can fix it by right-clicking on the file and choosing
Get Info. Then in the
Open With section of the File Info dialog, select Media Center 20 (if it isn't in the list, choose Other and then browse to your Applications folder to select it). Click the Change All button to set OSX to open all MJR files with Media Center (this is okay as MJR files are a proprietary file format for Media Center licenses).
Once you get it installed, you can copy the MJR file to other Macs and use it to license them as well. The MJR file (but not your License) expires after 14 days, but you can create a new one at any time if needed. More info:
http://wiki.jriver.com/index.php/Purchase_and_License_Recoveryhttp://wiki.jriver.com/index.php/Restoring_a_License