"What are demons? Are they fallen angels, dead people, or something else?", (Question from Taryn Leydon).
It's interesting that the origin of demons is never mentioned or described in the bible, at least to my knowledge. However, we can infer a number of things from the descriptions that are given of them. They are described as being bodiless spirits, that seek to inhabit the bodies of the living (Luke 11.24-26). They are described as being malevolent, and willing (if not eager) to cause harm (Matthew 17.14-18). They are also described as being in league with the devil (Matthew 12.25-29). Lastly, they are described not as dark energies or forces, but rather sentient spirits, that are capable of identifying themselves, and communicating with the living (Mark 5.7-12).
The most common explanation as to what demons are, is that they are fallen angels. However, this creates a number of issues. Angels (even fallen ones) have spiritual bodies, and presumably would have no purpose or ability to inhabit the bodies of people. Demons, however, are always described as being bodiless, and seeking to literally inhabit and commandeer the bodies of the living (Mark 11.24-26). This basically rules out demons as being fallen angels.
A more likely explanation is that demons are the disembodied souls, or ghosts, of wicked people. This is an unpopular explanation, but one that is much closer inline with the scriptural evidence provided about them. Whereas Satan and his angels still reside in heaven, demons are described as being from the underworld or dust of the earth, which is the dwelling place of the dead, "And thou shalt be brought down, and shalt speak out of the ground, and thy speech shall be low out of the dust, and thy voice shall be, as of one that hath a familiar spirit, out of the ground, and thy speech shall whisper out of the dust" (Isaiah 29.4 KJV bible). Familiar spirits are another term for demons. This verse associates demons with the underworld, indicating that they are the bodiless souls, or ghosts, of certain unrighteous people.
It is a common occult practice to both summon demons, and form relationships with them, often to obtain information and instruction. Notice how in Acts, there is a demon possessed girl who is renowned for fortune-telling, "And it came to pass, as we went to prayer, a certain damsel possessed with a spirit of divination met us, which brought her masters much gain by soothsaying...But Paul, being grieved, turned and said to the spirit, I command thee in the name of Jesus Christ to come out of her. And he came out the same hour" (Acts 16.16,18 KJV bible). The Greek word for demon (daimonion) is likely derived from the Greek "daio", which means to distribute fortunes.
Demons are often summoned out of the underworld to instruct one in occult secrets, and to give one information that they would not have otherwise known, "When they say to you, "Consult the mediums and the spiritists who whisper and mutter", should not a people consult their God? Should they consult the dead on behalf of the living?" (Isaiah 8.19 NASB). This is most likely the origin of demons; the ghosts of certain dead people who have been summoned out of Hades, and into the land of the living.
So why would God allow such a thing, as people to summon the souls of wicked people? God allows a lot of things to happen that people will have to answer for on Judgment Day. It's not in his nature to hit people with lightning every time they sin, but often to let things run their course, "The Lord knoweth how to deliver the godly out of temptations, and to reserve the unjust unto the day of judgment to be punished" (2nd Peter 2.9 KJV bible).
I should point out that it's also possible that demons have never lived in the flesh, but were placed in Hades by God, from some prior time. This may be the case with the locust army of Revelation 9. All we can really say with certainty is that demons are bodiless malevolent spirits, that will face God's wrath in the future, "...What have we to do with thee, Jesus, thou Son of God? art thou come hither to torment us before the time?" (Matthew 8.29 KJV bible).