Oh, this one is going to open a can of worms.
Library doesn't mean media files.
MC doesn't sync to a NAS when using just one copy of MC and importing media files from a NAS. You aren't running MC installed on the NAS as a MC Server are you, with the PC running as a MC Client?
If you aren't running a single copy of MC on your PC, connected to a NAS that contains all your media files, please describe how you are using MC, and how it is configured.
The real MC library, which is just a group of files stored in the location shown when you click on the library name under Playing Now, should always be on a fast local hard disk, not the NAS.
The library is actually quite small. For example, I have one ~40,000 file library which is a mixture of Audio and Video, for which the Library is about 30MB, while Thumbnails for the Library are about 350MB. Surely that would fit on your computer drive?
The Wiki is full of great information. Try reading through Getting Started, Auto Import, Library Management, etc.
Otherwise, I think I shall leave this one to you swiv3d !