Primary = earliest, original.
Primary Sources are first hand accounts, created at the time of an event or shortly afterwards. They are a record of what happened, or what was said, thought, or felt, during a particular time or event. The best primary souces were created as a result of the event (such as government reports or business records) or by an actor in that event, rather than someone watching from the sidelines. Participants in different roles will have different views of an event (a soldier in the trenches vs a General at Headquarters, for example). Sources may not exist for all points of view, but a historian has a responsibility to seek out as many different viewpoints as possible.
Primary sources can take many forms:
Something is not a primary source just because it is old - nor is a primary source free from bias, inaccuracy, or lack of authority. Each source must be carefully considered. Sometimes a source could be considered primary or secondary, and could be used either way. It's up to you to evaluate and decide what you want to do with that evidence.
Note that Primary Sources can mean different things for different disciplines. In the Sciences, they are articles documenting research done by the author, and for social sciences, they can be first hand accounts, primary research, or the first time an idea or theory appears in print.