Unlike OpenSSL and GnuTLS, which are crypto and SSL libraries, NSS is a more complete system with key management support, PKCS#11 support, etc. Rather than apps having to implement all their own key storage and management, they just use the existing libnss database and tools. Best of all, you can have a shared per-user key database, so you can FINALLY avoid having to install your X.509 client certificate manually into every app you use individually.
Key management in Linux is a shrieking nightmare for administrators and no fun for users either. I'd love to see libNSS more widely adopted as it'd really help address that.