Contemporary means "with the time" and literally refers to literature written during the lifetime of the reader.  So any literature can be described as cotemporary when discussing its reception at the time of its conception; for example, did Shakespeare's audiences ever see his plays as "contemporary literature"? Terms for literary periods are notoriously unreliable--so-called "modern" literature is now over two centuries old.  But it is safe to say that "contemporary literature" deals with current social and political problems, not historical ones.

The earliest extant literary works, those from ancient Egypt and Mesopotamia, date to 3000 BC. That means that when we study literature, we need to deal with some 5000 years of literary history. As an aid to understanding, and to dividing literary history into pieces that can be separated off and studied in individual courses, literary critics divide literature into "periods", or chronological groupings that seem to have some thematic or historical coherence. Twentieth century literature is divided into two major periods, "modern literature" or "modernism", referring to the literature roughly from the death of Queen Victoria to the end of World War II and post-war or contemporary literature. Thus a contemporary author is one whose major work was published after 1945.