The Hebrew Bible (a.k.a. the Old Testament), in the traditional Masoretic version, is annotated with a complex system of cantillations, which serve as a combination of punctuation marks and musical notes, supplying both a melody for chanting the Hebrew text of the Bible as well as indicating the prosodic structure of the sentences.

Actually, there are two systems: one for the books of Psalms, Proverbs, and Job (well, almost all of Job; a few verses, the prose ones, are in the other system), and one for all the other books. It appears that the distinction is one of prose vs. poetry, and may be related to the length of the verses: verses in the three "poetic" books tend to be shorter. (Then again, there's poetry in the "prose" books as well).

The prose system is by far the best understood, since religious Jews still use it as a melody when chanting the Bible in synagogue. Each tradition has its own particular way of actually performing the cantillations though (i.e., each cantillation is its own musical motive, but the precise notes and contour vary from tradition to tradition). There are also different versions within the same tradition for different parts of the Bible (e.g., Ecclesiastes, Esther, Pentateuch, etc.) The performance of the poetry system is no longer preserved in most traditions, though the Yemenite Jews still have a version of it.

There is someone (one Daniel Meir Weil) who has claimed to have reconstructed the "original" performance of the cantillations; believe it if you will.

The system works by hierarchical binary subdivisions of the phrases... mostly. So there are some cantillations that indicate a break of some kind, and some are stronger than others, and some that are connectives that link words together. It's not quite so simple as that, since there are musical considerations which forbid or require certain combinations. Also, the subdivision doesn't work in the obvious way: the subdivision before the division of level X is marked by level X-1, but the subdivision after it is marked by level X. It makes sense, in a certain way, really.

In my opinion, the greatest modern authority on the subject is Rabbi Mordechai Breuer.