In medieval times, incubi were thought to be angels that had fallen from heaven because of their insatiable lust for females, and who roamed the earth in search of humans to satisfy their lust. An incubus would often rape a woman in her sleep, but if she woke, he could inflame her with desire, causing her to comply willingly. Others thought that incubi were not fallen angels themselves, but the unholy offspring of fallen angels and humans.
The offspring of an incubus and a human was a deformed creature of some sort: deformed children, witches, demons, and half-human, half-animal creatures. Merlin, the magician, is a possible example*. Twins were also sometimes considered to be evidence of a visit from an incubus.
Since some interpretations took incubi to be non-corporeal beings, it was thought that they must enter and animate the body of a human, either dead or alive, before they could do anything. (There is at least one case of a man, Bishop Sylvanus, successfully defending himself against rape charges on the grounds that he was possessed by an incubus at the time). This also implied that the incubi could not fertilize women with their own seed, only with that of human men. It was believed that this seed might come from succubi who had seduced men; perhaps demons could even change sex at will, and the succubi and incubi were all one type of demon.
There were a few clues that could tell you if a 'person' was an incubus. They had magical powers, the most common being the inducing of lust and causing other people in the house to fall into a deep sleep. They also often had unusual genitalia; unusually large, icily cold, made of iron, or double-shafted.
Unlike many creatures of the dark, incubi are largely immune to religious artifacts, prayer, and exorcism.
"Incubi do not obey the exorcists, have no dread of exorcisms, show no reverence for holy things, at the approach of which they are not in the least overawed... Sometimes they even laugh at exorcisms, strike at the exorcists themselves, and rend the sacred vestments."
-- Ludovico Sinistrari*, 17th century Franciscan friar, Demoniality.
* Ludovico Sinistrari also claimed that Martin Luther was the offspring of an incubi (although he probably didn't mean it literally). Martin Luther himself believed that deformed children should be killed, as were the offspring of demons. Incubi, succubi, and other demons of all sorts were oft debated by most of your favourite theologians.