Dō (literally: “the Way”) is a path which leads to enlightenment.
Dō is the Japanese pronunciation of the Tao which Lao-tzu spoke of the in the Tao Te Ching, which typically manifests itself in arts which are practiced as a way of life. Karate is one of many Ways, but keep in mind "that which is called the Way is not the True Way, for the True Way cannot be named."
Dō is a difficult concept to explain, since Western civilizations do not use arts, crafts, or sports as a means for teaching spiritual or ethical truths. The closest equivalent of dō in Western philosophy would be to achieve araté through phronesis. Dō and jutsu are permanently linked, like the two sides of a coin -- however they are complements, not opposites. Dō is not opposed to jutsu; a serious commitment to jutsu will gradually reveal dō through a series of epiphanies.
Zen Buddhism was never popular among the Okinawans. Zen and karate were linked in the 1920s by Gichin Funakoshi, in order to make the art relevant to the modern world, per the request of the Dai Nippon Butoku Kai.
Americans tend to overemphasize Zen, usually due to idealizing Asian culture. Surprisingly, the animé fans aren't to worst offenders -- it’s the middle-aged “spiritual-but-not-religious” people on quests “to explore warrior energies.” These seekers want to talk instead of train, but the truths they seek can’t be expressed with words. It’s an experiential thing, like getting a joke. It’s not the joke which enlightens; it’s the “click” of getting the joke. No one can "seek wisdom," because wisdom only comes from within, as a result of dwelling upon your life experiences. Martial arts are thus a philosophy class for kinesthetic learners -- a bookmobile-like outreach program to bring philosophy to those who would normally pass it over and/or would not have access to it. Everything in the martial arts has a practical and a philosophical significance, so wisdom can become available to all -- but only after a workout, because the workout is the enlightenment. Enlightenment cannot be found, because enlightenment is a verb, not a noun; enlightenment is not a thing or a possession. Enlightenment isn’t a prize you can display or brag about; it’s a weird dream-like moment of clarity, which you can never really explain to other people. Even if you become enlightened, you must continue along the path, as there might be a deeper enlightenment beyond what you've experienced. However, these are lessons which go unlearned; upon realizing that martial arts masters are regular-ass people with day jobs, these seekers quietly see themselves out and find a new castle in the sky.