The current Alpha versions of MC Mac do not require licensing, so you don't have to worry about it at all at this point.
However, when you purchased MC Mac, the license information was emailed to the address you registered. In the future, when MC Mac does require licensing, it will have a system built-in to handle the license restoration. Basically, the way it works on Windows is:
1. You have a license key (you already have this). This is a "serial number" for your copy of MC, which never expires.
2. To apply this license key to a particular copy of MC, you use a special MJR file. When you made your purchase of MC Mac, one of these MJR files was emailed to you.
3. These MJR files do expire after 14 days, but you can make a new one at any time from within MC by choosing "Restore from Internet" and entering your License Key. This process is called a "Restore". Once you have a valid MJR file, you can use it to license as many copies of MC as you'd like within that 14 days (within reason, they should all be on computers you own and control).
4. You can perform up to 10 of these "Restores" per year. This limit is just to keep those who would try to game the system to install copies of MC on an entire office-full of PCs with only one license at bay. If you're not doing anything nefarious, don't worry about it. If you ever run out of Restores for some reason, just come here to Interact and post an explanation of what happened. The JRiver folks can reset the Restore count and get you fixed up.
Hopefully this helps explain the process.