The reason for libraries carrying multimedia is twofold:
1) Patrons: As someone mentioned, Patrons aren't coming to libraries for books anymore. Not for the most part. DVDs and other media are a way to get younger patrons in, and to get them using the libraries.
2) Research & Archiving: Multimedia is also the future. Libraries, in theory, are repositories of knowledge. As such, books alone aren't enough to fully understand or appreciate many topics. Music, Videos/Movies, and other means of media are needed to full experience a topic. Also, research in media has allowed us in media studies fields to examine these other forms of media in the same light as a book or research article, that is, they've gained legitimacy as usable materials in research. As such, just as libraries keep records of old local newspapers on microfilm, DVDs and VHS are being kept now for archiving purposes.
I work in a library, and I can say that our media section is one of the smallest parts of the library (in terms of staffing and material) but also is one of the most heavily trafficed