I'll try to write something brief for those that don't want to go off to that other website.
Linear editing usually refers to tape-based systems where the data (audio/video) occurs in sequence from beginning to end. For example, to insert a section of audio in a linear editing system you would have to shuttle the tape to the right location, cut the tape, and insert the extra tape of audio you want to add in between the two cut pieces.
Non-linear editing typically refers to computer-based systems where data can be found instantly without regard to the sequence it was recorded in. Using a parallel example, you can accomplish the same kind of edit on a digital system by jumping immediately to the appropriate place (assuming you know where that is), cutting and pasting audio data wherever you want to, overwriting, inserting between, or blending with whatever's there already, etc. Usually this is all saved internally by pointers to audio data and the edits are applied non-destructively, that is, the original data is still there and you can undo anything.
Whew, it is hard to explain in just a few sentences. I think you had the right instinct, pratt...