The K-Lite Codec Pack 64-bit is a collection of 64-bit DirectShow filters that can be used along with 64-bit players, such as Windows Media Center.
Please note, this may not be necessary to get videos or audio files in general playing on your system. Even if you have 64-bit Windows, it will run 32-bit players perfectly well, and in fact those 32-bit applications won't be able to use the filters in this package anyway. Which is why the K-Lite developers recommend that you use the regular K-Lite Codec Pack "when possible", as it "contains more, better and faster decoders".
If you're still having problems with 64-bit players, though, there's no harm in installing the K-Lite Codec Pack 64-bit as well. It can run alongside the 32-bit edition quite happily, without causing any problems or issues.
Otherwise, though, the package includes all the usual bits and pieces to help you play all the most common audio and video files: ffdshow, AC3Filter, AC3File, Haali Media/ LAV/ Matroska splitters, DirectVobSub and so on. And of course troubleshooting options like the Codec Tweak Tool are on hand to review your setup and try to detect and fix any problems you might have.