According to the Oxford English Dictionary, "In the context of academic research or writing: designating source material contemporary with the period or thing studied; designating an original document, source, or text rather than one of criticism, discussion, or summary."
To put it another way, primary sources are the original records created at the time of historical events (or, in the case of memoirs & oral histories, by the participants after the event happened). They can be letters, manuscripts, diaries, journals, newspapers, speeches, interviews, memoirs, documents produced by government agencies, photos, audio, video, research data, or objects/artifacts.
Secondary sources interpret, analyze, discuss, or comment on primary sources. Secondary sources are the interpretations of the event created by someone without firsthand experience. They are at least one step removed from the event, study, or work. Examples of these include scholarly articles, reviews, reference works (such as encyclopedias or textbooks), biographies, and newspapers, etc. .
Primary sources differ from discipline to discipline. Some examples of primary sources from various disciplines are listed below:
Social Studies/History:
Letters, diaries, journals, memoirs, personal narratives, oral histories
Newspaper coverage at time of event, speeches, interviews, photographs, recordings
Artifacts such as period clothing, furnishings, tools, weapons
Science:
Original scientific research studies, laboratory notes, proceedings of conferences, and dissertations
Literature/The Arts:
The original work – books, stories, poems, plays, music manuscripts, works of art
Mathematics:
Census counts, store records, school texts and ephemera, scientific notes