A variant spelling of
magic used by many
neo-pagans to distinguish between
stage magic, which is primarily
sleight of hand and
illusion, from "real magic," which is much more subtle but also has a much wider range of uses. Other spellings I've seen are "majik" and "majic."
Aleister Crowley and others define magick as using one's will to alter one's environment. This, however, includes sending a nerve signal to your arm to make it reach over and pick up that can of soda. Crowley, I'm told, would say that that is also magick, but most people want a more specific definition. The best I can think to say is that magick takes effect through means that are not physically perceptible. Common uses are finding love or work, healing, and transformation of the self (ex. breaking a bad habit). It is most effective for enhancing a more mundane task; for example, doing a spell to get a job won't help you unless you also go look for one.
Methods of magick can essentially be boiled down into two primary forms: spellcraft and energy work. More detail can be found in the individual write-ups.
Spellcraft is using specific tools, words, etc. to achieve the effect (I don't mean dance around and yell "booga booga" and turn someone into a frog!). Common methods are candle-burning, dancing and chanting, and making poppets (voodoo dolls are one possible variety, but most modern witches will tell you that it is a very bad idea to do any harmful magick). It is good for beginners who haven't learned to sense the energy directly, and for long-term goals like job-hunting.
Energy work is more direct and is often referred to as psychic powers: sensing, like empathy, aura reading, ESP; and affecting, like weather-work and healing (though any type of affecting work can also be done via spellcraft). The distinction between this and spellcraft is that energy work is done entirely in the mind. Tools may be used to help focus, but they are not essential. One important note is that everyone can learn to do it (whereas some think that psychic powers must be inborn), although they may have different ways of sensing the energy.
Arthur C. Clarke said that any sufficiently advanced technology is indistinguishable from magic. Terry Pratchett replies that any sufficiently advanced magic is indistinguishable from technology. There are those, me included, that believe magick is just science we haven't figured out yet.