A primary source is usually a record made at the time of an event by participants or by firsthand observers, but a primary source might also be created many years after the event in the form of an autobiography, memoir, oral history, published papers, etc. (For example, The Collected Works of Abraham Lincoln was originally published in 1953, long after Lincoln's death.)
Examples include, but are not limited to:
Primary sources can be very different for different subjects. If you are writing a paper about an early female physician, for example, then her diary would be a primary source. If you are studying mid-twentieth century diplomatic history between the United States and Iraq, State Department records (such as Confidential U.S. State Department Central Files: Iraq, 1955-1959, available on Microfilm 498) would be a primary source.
If you are unsure what constitutes a primary source for your class, ask your instructor for some ideas. Also see this site from Yale University for helpful hints on finding primary sources: http://primarysources.yale.edu/