Witchcraft is an ancient style of magick, that has been as changeable as magic(k), itself. The word comes from the Old English term for "wise one," which had been wicca (pronounced with a CH sound). Forms of witchcraft vary, but most of the typical characteristics that we know today are rooted in Celtic and Pagan beliefs. During the time the English had occupied Scotland, parts of Ireland and eventually the Americas, a newer tradition called Anglo-Celtic witchcraft emerged, as cultures mingled. This combination of beliefs is ultimately what we commonly refer to today, as "modern witchcraft".
One must take note that this is a magickal practice and not a form of religion, so any spiritual orientation may have aspects of witchcraft there-in - see also, Wicca.
Witchcraft as a practice, is a form of low magick, which tends to take a different path than that of High Magick. Witches tend to use spells that require herbs, potions and "charms", with little preparation. Such spells have very little or no ritual orientation, so the elaborate chants and Astrological association may not apply. In this paradigm, witchcraft deals in the realm of Nature and all the energies contained within the materials used. However, High Magick is more within the realm of the heavens and seeks to align with a "higher power".
Because of the strong Celtic influences behind this, it may be difficult to apply the term witchcraft to other cultures, although it can be done. Certain shamanic, Voodoo and Christian practices may be deemed as witchcraft, for example.