|“||In the poison'd entrails throw.— Toad, that under cold stone, Days and nights has thirty-one; Swelter'd venom sleeping got, Boil thou first i' the charmed pot!||”|
Witchcraft, formally defined by anthropologists and those who study human religions, is the use of rituals and magic to accomplish some kind of ends on this earth, most often curses which can refer to either sex but more frequently means a woman. In modern lay idiom, it is largely associated with various sorts of neopagans, such as Lucy Cavendish and Wicca. A man who acts similarly is a wizard or warlock or simply a male witch. In the American folk / entertainment world it is the evil wrought by women onto poor suffering men who cannot resist such temptations.
By definition, witches directly work upon the world through spells to do their own will. This differs from priests, who are intercessors between a god or gods and the people. Priests pray or do rituals to ask the god to change the world. Witches also differ from herbalists in that they are invoking magic. There is no reason any particular witch cannot also be a priest/priestess or herbalist.
Virtually all religions have a role that anthropologists would call a "witch," and it almost always is a person dealing in darker or so-called "evil" or unsanctioned elements of the religion. Historically, many religions used the concept of witch to explain diseases, untimely death, droughts, and other unexplained negative circumstances that effect an individual or society. Divination may be used in an attempt to find the witch/sorcerer believed responsible for some calamity and retribution likely happens to the assumed witch. Socially deviant people are more frequently accused of witchcraft and this works as a social control. 
Christianity and witchcraft
Christian theologian Augustine of Hippo didn't believe that humans or the devil could do any magic at all, leading to relatively little persecution of witches when he was popular. Later theologians like Thomas Aquinas took witchcraft seriously (Aquinas associated it with sex), making witch-hunts much more common. Witchcraft was considered devil worship and a sin against the First Commandment. Protestants and Roman Catholics both tortured and executed people mostly women, accused of witchcraft. 
Modern western views of witches generally comes from the Christian view, where a society's undesirable women, were tainted as "witches" and blamed for the misfortunes of society. Simple herbalists, midwives, as well as the mentally ill were frequent targets of being "witches" - or women who associated with the Devil. The Black Death was largely blamed on witchcraft in the 14th Century; the Salem Witch Trials became an expedient way to eliminate political problems and blame women.
In the 21st century people are more inclined to look for scientific reasons why things go wrong but Roman Catholics  and extreme Protestants still believe in witchcraft. For example Harry Potter causes regular protests from more hysterical sections of Christianity. 
The bible's view on witches
Anyone taking a literal view on the Bible should take into account these quotes:
- "Thou shalt not suffer a witch to live." Exodus:22:18
- "A man also or woman that hath a familiar spirit, or that is a wizard, shall surely be put to death: they shall stone them with stones: their blood shall be upon them." —Leviticus:20:27 (KJV)
So witches should be burned at the stake or better stoned as we speak. That just shows why taking the Bible literally is bad.
- Douglas Linder. A Brief History of Witchcraft Persecutions before Salem. University of Missouri-Kansas City. 2005.
- For example, in traditional Navajo culture, the "good" user of magic is a Singer, the "bad" user of magic is a witch (regardless of gender).
- Magic and Religion
- All Witchcraft Is Satanic!
Adapted from an out of date version of a RationalWiki article