Linux Mint was started in 2006 and at present, is the forth most widely used Operating System after Windows, Mac and Ubuntu. There has been development ever since it started and different versions have been released. The one thing to notice to these version names is that there is a unique logic to each of it.
Codenames in Linux Mint are always a female name that ends with the alphabet "a". These Codenames follow an alphabetical order and the first letter of the codename corresponds to the index of the version number in the alphabet.
Since version 5, Linux Mint has followed a 6 month release cycle. The version number is increased by 1 every new release.
Here's a list of the versions that have released for Linux Mint and their codenames. You can clearly guess the version numbers and the codename logic associated.
When a minor update is rolled out, the codename starts with the same alphabet and ends with "a", as in the case of Barbara, Bea and Bianca. Similarly for the versions 3.0 and 3.1 releasing under the codename Cassandra and Celena.