BaseElements 15 is a paid upgrade from version 4 or earlier. The current version is 15.0.3, you can view the release notes.
The standard fmp12 files require a copy of FMP or FMPA version 14 or later and have sharing enabled, so can also be used on FileMaker Server 12 or later. Sharing can be turned off in the files if it's not required.
Single User Runtime Application
The runtime is built with FMPA 15, so has the same requirements as FMP 15.
If you own a previous version of BaseElements 4 or earlier you qualify for upgrade pricing. If you purchased BaseElements during the 14 beta your licence will work with 15 and there's no upgrade cost.
If you're having any issues, check out the support pages for more details.
BaseElements 4 for FileMaker 12
BaseElements 3 for FileMaker Pro 11
You can still download BaseElements 3 for FileMaker Pro 11 if you are not yet running FileMaker Pro 12.