Back in the late 80's I was hanging out at Sommerville Community Access Television, and learning to edit video tape on 3/4" U-matic equipment using three decks and a switcher. Having previously tried to edit 8mm video using a camera and a playback deck, it was quite a step-up for me.
Then one of the staff got a job at a company called Avid. We were told that Avid was working on something called "non-linear editing."
One day some months later, I went out to see a demo of the Avid software and I was blown away. Even though the video being played back on the screen was low resolution - not even SD resolution, let alone what we see when we edit HD these days - and even though their product was aimed at film editing, it was obvious that this was the future of video/film editing. Being able to randomly access your content, apply transitions and review your work almost immediately - and then change it just as quickly - was astounding.
Going back to the "old ways" after that demo was awfully disheartening and frustrating - Adobe Premiere didn't arrive until the end of 1991.
MacVideo.tv has an interview with Bill Warner, one of the founders of Avid, where he talks about how the company got started: Bill Warner - the man who "made" AVID