Legal deposit libraries have a legal arrangement to receive a free copy of every book published in the country in which the library is located. This practice seems to have begun if France, where a law written in 1537 declared that no book could be distributed without first being deposited in the king's library.
The first English language library to have this arrangement was the Oxford University Library which, in the early 1600s was curated by Sir Thomas Bodley. Bodley established a policy with the Stationer's Company to have a copy in the university library of each book published in the UK. This library was renamed the 'Bodleian Library' in his honor.
The United States currently has the Library of Congress as its one legal deposit library.