Like BobbyJ, when I first heard the term I was horrified at the idea. I didn't understand what it meant - I saw it as "giving up on my husband". It took a long time and several failed attempts at a reconciliation to finally reach a point where I could see "no contact" meant letting go of the chaos and drama that filled my life.
Some people do this very well while remaining in a relationship with their A's. I've seen it in Al-Anon. They have a kind of shut-off valve to the addict BS and don't get enmeshed in it. It just rolls off them like water on a ducks back. Those people really impressed me. Funny thing is, those folks were impressed by me leaving, too. That was an eye opener!
In the end, going no contact for me meant giving up on it all. I was done. There were literally no words left in my head to continue even trying to converse. It was futile arguing with him and his distorted thinking. It was time to let it go. Been 5 months now - the divorce is final, and although I sometimes get extreme urges to reach out, to get "closure", to ask, again, "why?!", I don't. Because now I know the result of that, and I won't go back to that dark place again.