A primary source is one that comes directly from the concept or people in question.
In the field of history, this means works created during the time period in question, whether it's from a person who is recounting an event they lived through or a secondary source from that historical time period (e.g. a newspaper article from 1864). Primary sources give us direct glimpses into how people thought and felt at the time.
In government and political science, the text of laws, bills, statutes, and court opinions are primary sources. In the sciences, primary sources include reports of original research and lab notes. In English/literature analysis, the text of the analyzed work, even if it is fiction, is a primary source.
However, good research includes a mix of primary and secondary sources. Secondary sources written at a later date have the benefit of historical perspective or broader source material, and, sometimes, emotional distance that the primary source creator lacks.
Since such a wide range of materials could be considered primary sources and the definition can be so broad, you should check with your instructors to make sure a source fits their understanding of a primary source before using it in your research.