Library of Congress essentially does three things:
As people have said, it is the copyright library. It gets a copy of every book copyrighted in the U.S., but it only keeps the ones the librarians there choose.
It is also, duh, the library of Congress. Congresspersons and their staff can check out books and do research there. There is a section called Congressional Research Service that has tons of experts who do nothing but answer questions for congresspersons. I remember reading about scandalous rumors that they wrote term papers for congressperson’s kids, but that was long ago. This page links to some CRS reports that have been made available to the public.
Finally the Library of Congress is sometimes called America’s Library. Its wonderful website America’s Memory makes that claim look pretty reasonable. They also provide some services to libraries around the country. To be brief they provide cataloging and they also manage the Library of Congress classification system (used by libraries too big for Dewey Decimal).
The bitter joke among librarians is that when LC wants a bigger budget they claim to be America’s Library, and when one of America’s other libraries asks for service they claim to be just Congress’s library.