Nowadays the popular image of a witch is a woman dressed in black (either old and ugly, or young and promiscuous), with a demon possessed black cat which does her bidding (usually at the cost of her soul upon death. . . or basically no cost at all). Often they use their magic to pursue love, riches, or power.
But wait, according to historical records, that is not what people believed during the infamous European witch trials! Though around 75% of witch trial victims were female, anyone was likely to be accused; but in a male dominated society controlled rich men and clerics, it was easier for women to be the scapegoats.
One of the biggest differences between the modern view of such witches is that of the familiar. The familiar in literature (such as the Hammer of the Witches) and popular imagination was a demon, or Satan himself, which generally approached the witch and tricked or forced them into his service. Such demons may appear as a cat, but often also a dog, a toad, a hare, or pretty much any animal commonly found in the area.
The familiar often offered love, riches, or power, but these things never turned out to be real. The familiar of the past was not satisfied with taking orders either, and commonly those accused of being witches 'confessed' that the demon would punish them when they failed to bring harm to others, or failed to select people for their familiar to attack.
The witch wasn't necessarily irredeemable either, especially in early trials when they might be given a chance to prove themselves to no longer be practicing witchcraft and loyal to the church once more. Other times, the act of execution was even considered to redeem their souls.
Resources and Further Reading:
Alexander, Dominic. Spell Bound. Readers Digest, 2002.
Briggs, Robin. Witches and Neighbours. Penguin Books, 1996.
Wikipedia, (last modified 2015, 8, 18)