Linear Editing vs. Non-Linear Editing
Non-linear editing is in opposition to linear editing. Linear editing was the original editing system, where actual pieces of film stock where cut and spliced together to make the final film. What this meant is essentially that you had to go through the film, making the edits, and could not go back and change them. You had the ability to preview the changes, but if you wanted to go back you were really out of luck.
The non-linear system changed this and turned editing essentially into a file storage and reference system. With a non-linear editing system, which is really just editing software, you capture or import all of your media and then the program references it for film construction. You can cut together and alter whatever you want and it is not permanent, although you can save your changes to the final film. No changes you make permanently alter the source material.