“Mushin” is a Zen-influenced concept in the Japanese martial arts, particularly the art of swordsmanship. The opponent moves to attack you and you suddenly perform a technically perfect counter that cuts him down with a single strike, yet you never consciously think about what strategy you're going to use. That's called “mushin” or “non-thought.”
It doesn't literally mean the absence of thought, because if you perform some technically complex fighting technique with perfect timing and application, thought of a highly efficient kind is obviously involved. What it means is that there's no conscious thought, no self-awareness to interfere with the technique. It almost seems like it happens on its own, although its actually the result of years of training and discipline.
This isn't really as esoteric as it probably sounds. Do you think an NBA player is consciously thinking out every detail as he sinks his tenth basket of the night? No, of course not. In the course of his career, he's put the ball through the basket so many times that he doesn't need to consciously think about it. He just does it. That's “mushin,” and it works the same way in swordsmanship.
After years of technical training, the swordsman absorbs technique so deeply that he can perform perfectly under high stress without thinking about technique. If he didn't learn the technique first, he wouldn't be able to do that. That's why untrained pseudo-swordsmen who fantasize about starting their own sword style are generally not taken very seriously in the world of Japanese martial arts. Mushin is something that happens after a lot of training, it's not a substitute for it.