According to JewishEncyclopedia.com, siyyum is:
The formal ceremonial act of completing the writing of a scroll of the Law, or the formal conclusion of the study of a division ("massekta") of the Mishnah or Talmud. In the former case the ceremony is called siyyum ha-Sefer; in the latter, siyyum massekta.Either way, it's the celebration of the completion of a book. What a marvelous concept, especially for a people that highly value education and language, and claim to be of the book!
Now obviously not just any book is grounds for celebration; stopping for a party every time I finished a comic book on a Sunday afternoon would get exhausting, and some books I have celebrated completing only because it meant I didn't have to read them anymore (I'm looking at you, Wide Sargasso Sea!). The concept originates in the Talmud and clearly carries the implication that one has been reading sacred books (and really, what else would one want to read?). I believe, however, it is allowable and proper to expand the concept to include any well-loved book or rigorous course of intellectual development. I would not look askance (much) at a friend that had a siyyum upon completing the Harry Potter series, especially, at this point, if the point of the celebration was finally catching up on the past 15 years. Likewise, a friend that had just finished working through a MCAT prep book would be well justified in throwing a siyyum.
A more interesting question would seem to be, in our increasingly multimedia age, does it have to be a literal book or will any similarly challenging academic pursuit qualify? If one has a siyyum for the Potter books, what about for the Potter movie? For completing a difficult post-graduate course? I am torn on this. On the one hand, the siyyum is celebrating learning, which would suggest the medium is unimportant; on the other - and this might be because I am a sentimentalist - it seems to lose much when divorced from the concept of a book. I therefore have somewhat of a compromise position: I would personally only hold a siyyum for a book, but would not begrudge a friend that wanted to celebrate something else.
I also see value in embracing the siyyum as a national practice, regardless of religion. The siyyum could make reading cool again. I referred to the Potter books because when they first came out many people were thrilled that they were getting kids to read again. Rather than wait for the next mega-popular book series to come along, the siyyum heightens the concept of reading itself, regardless of what one reads. I can see teachers using this in school; would students be more willing and eager to read the classics if there was a class party waiting at the end?
The modern book club could be seen as a form of siyyum. In theory, most book clubs select works of some academic or social importance (it's debatable which of these Oprah's imprimatur would be). The group then comes back together to celebrate and discuss; that seems to be exactly what the sages were describing.