Linear is destructive editing. Non-linear is non-destructive editing. What's that mean?
If you need to make a cut to your track, will you use a razor blade on magnetic tape, or a right click of a mouse? If you mess up on the computer, no big deal, press undo. However, if you cut the tape in the wrong spot, you better think of a creative solution, because there's no going back now.
Imagine a life where you could just press undo if you made a mistake. Wouldn't it be great?
Probably not. Sure, it would be much easier, but also much less interesting. Say goodbye to crime dramas, comedy improv, sports, and probably most children.
The implications of non-linear editing have been staggering on music production. Why? Because you can always press undo and fix your mistake. Because of this, many imperfections of music have been weeded out. But it's the imperfections in the recording process that add drama, soul and nuance to the track! Great examples of mess-ups in the studio are Peter Townsend and Roger Daltry singing "it's an Eminence Front" at different rhythms, Sting laughing after accidentally sitting on a piano while recording Roxanne, or Ringo Starr shouting "I've got blisters on my fingers!" after recording the umpteenth take of Helter Skelter.
Because splicing tape was such a pain in the ass, it put extra pressure on the musicians to perfect their craft before entering the studio, thereby producing a greater performance in the studio. And yes, sometimes this also meant keeping in mistakes if the performance was too good to scrap. Let's call these mistakes "artifacts." These artifacts become cherished little moments the 30th time you listen to the track.
These days, you can easily polish a turd in ProTools. A great performance is no longer required. Just press undo.