When I started working at a library at my college, I at one point remarked to the reference librarian that she seemed to contain all human knowledge in her brain. She said, no, it was just her job to know how to find all human knowledge.
This was a teeny-tiny library, and we only had four librarians.
The Director: she is in charge of the library. Amongst other things, she was the one who told the college administration how much money the library needed, and decided which department of the library got how much. Basically any major decisions went through her, and all money stuff. She was also the ultimate authority in what books were purchased, replaced, sold at the book sale, etc.
Acquisitions and periodicals guy: He, uh, acquired things. This included managing subscriptions to about a hundred periodicals, which also meant deciding how many back issues of each periodical are kept out (ie, past six months of Time are open to the public, but only the past month of the local paper), how many back issues of each are kept in storage available upon request, and when to clear out old back issues for the sake of space. He was also primarily in charge of buying books - adding new items to our collection, deciding whether or not to replace lost or worn out items, and buying new copies of very popular items.
Cataloging/Tech Services: Once we got the new items, she made them usable. The first step is to figure out where it goes - some books do already have an LOC number, but some can also fit in multiple places, and it depends on the particular library. The book needs to be added to the catalog (both the computer and an actual hard-copy list), labelled, stamped, barcoded, and in many cases you need to put a protective cover on it. Once books are in circulation, they need constant looking after (rebinding, repairing taped pages, pulling the hopeless cases from the stacks, replacing the anti-theft strip, cleaning DVDs and CDs, etc.) Most of the actual tech work was done by student employees, in this case.
Circulation/Reference: What you think of when you think of a librarian. She checked out books, kept the database of patrons current, sent nagging letters at delinquent patrons, send us students to search for missing materials, sent us students to keep the stacks in order, lorded over the interlibrary loan program, and could tell you how to find just about any information (look online, look in archived periodicals, look in this or that online database, “Oh here, this book should really help you with that paper you’re writing”).
Again, this was a very small college library, so we had fewer staff than a bigger library, and most of the day-to-day grunt work was done by us student employees. In bigger libraries, the work is divided up - the public library in town has three branches, a collection ten times larger, and several dozen librarians. So the specifics vary, but the basic theme of the jobs stays the same.