What are Demons?

Demons are evil spirits that are part of a highly organized satanic kingdom on earth and in the heavenlies. This kingdom is ruled by Satan and has a specific hierarchy of power (Ephesians 6:12, Ephesians 2:2; Matthew 12:24-27). The definition of the Greek word for demon, daimonion (Strong's #1140) gives us more clues about what a demon is:

the divine power, deity, divinity
a spirit, a being inferior to God, superior to men
evil spirits are the messengers and ministers of the devil
Origin: There are two theories about demonic origin that I'd like to highlight. Both theories hold that demons are created beings who rebelled against God:

Fallen angels: Satan, formerly Lucifer, was the “covering” cherub of the throne of God (Ezekiel 28:14-16). When he sinned by pride, he persuaded a third of the angels to rebel against God (Revelation 12:4). Satan and his angels were cast out of heaven to earth (Isaiah 14:12, Ezekiel 28:16-17, Luke 10:18). This theory proposes that demons are the “fallen angels.”
Disembodied spirits: Isaiah 14:12,16,17,20 suggests that Satan was the leader of a race of beings prior to Adam. Ultimately this race was destroyed by God with a worldwide flood, explaining the condition of the earth in Genesis 1:2 (dark and covered with water). This theory proposes that demons are the disembodied spirits of the pre-adamic race.
Regardless of their origin, the fact is that demons exist today just as during Jesus' ministry. The Bible gives us much guidance on how to deal with them under the authority of Jesus Christ.

Characteristics of Demons:

The demons that we encounter on earth seem to prefer to inhabit bodies (Revelation 18:2, Matthew 12:43-44, Mark 5:12).
Communal: Demons often live and work together. Jesus explained that when re-inhabiting a former host person, a demon will take seven spirits more wicked than himself and reoccupy the person (Matthew 12:43-45). Examples of communal demons are found in Mark 16:9 (Mary's seven demons) and Mark 5:9 (man with a legion of demons).
Demons have intellect and will (Matthew 12:43-45; Mark 5:6-13)
Demons vary in level of wickedness (Matthew 12:43-45; Mark 5:6-13)
Vary in power level and endurance: they require rest (Matthew 12:43-44; Mark 5:6-13); some are only routed through prayer and fasting (Matthew 17:21, Mark 9:29)
Recognize that Jesus Christ is the Son of God and those operating in his authority (Mark 1:24-26; Mark 5:10-13; Acts 19:15)
Capabilities of Demons

Can travel (Matthew 12:43-45)
Can cause sickness, disease, fever, physical abnormalities, mental torment, alterations of voice
Can fight with God's angels (Daniel 10:13,20; Revelation 12:7)
Can influence human events (Revelation 16:13-14)
Can speak through a person’s voice and see through their eyes (Acts 19:15)
Can affect the "state" of their host person (Matthew 12:43-45) ranging from total possession (Mark 5:2-8) to periodic influence (Mark 9:17-18). They are able to influence the emotions, thoughts and actions of their host toward destruction. Examples include the Gerasene demoniac cutting himself in Mark 5:5 and the boy who was being thrown into the fire in Mark 9:22.
Can invigorate people with extraordinary strength (Acts 19:16)
Can deceive people and draw people away from the truth, enticing them by their own desires (2 Chronicles 18:20-22, Luke 4:1-13, James 1:14 inferred, Acts 5:3)
Why do demons access humans?

To fulfill their master’s mission: Satan, also known as Beelzebub, is the ruler of all demons (Luke 11:15-20; Matthew 12:24-27). Satan’s mission is to steal, kill and destroy (John 10:10). Likewise, demons will try to steal, kill and destroy whatever they can ( Luke 11:17-18). They will also attempt to take people captive by deception to do the Satan's will (2 Timothy 2:25-26).
They desire a body: Bodies apparently offer demons rest and/or shelter. Jesus explained that after being cast out of a body, an unclean spirit goes through dry places seeking rest and finds none. It tries to return to the person it left (Luke 11:24-26; Matthew 12:43-45).
God allows them to for judgment purposes: Saul's tormenting spirit (1 Samuel 16:14); lying spirit & Ahab (2 Chronicles 18:19-22); Jehoram's fatal illness (2 Chronicles 21:12-15)
To oppose God's plans and purposes: Demons are often sent to try to block or thwart God's servants. This can manifest in many ways including depression, sickness, confusion, temptation, doubt, etc. The purpose is usually to weaken faith (2 Timothy 1:5-9), since faith is the key ingredient for fighting spiritual warfare.
How do demons access humans?

Our sin gives them "legal" right to enter: Sin gives demons footholds in us for oppression. Jesus told the sick man, “Go and sin no more, lest a worse thing come upon you” (John 5:5-14). Bible examples of other sin footholds for demons: 1 Samuel 15:22; 1 Samuel 16:14; Luke 22:3-6; Acts 5:2; 1 Timothy 6:9-10; Numbers 5:18-30.
Curses from sin (1 Samuel 14:24; Numbers 5:18-28; Genesis 9:24-25; 2 Samuel 6:20-23): Our sin can bring curses upon us and our descendants. Demons are empowered to work according to these curses. For example, patterns of sexual sin like divorce or adultery can often be traced down through family histories.
Trauma: Spirits of fear can access us during traumatic events. Since faith acts a shield, fear (faith's opposite) weakens the shield when we doubt God will protect us. This leaves us vulnerable to a spirit of fear. One of Satan's principal objects is to take people into bondage to fear (Romans 8:15; Hebrews 2:14-15).
Violated oaths (Numbers 5:18-28; Matthew 5:33-37; James 5:12): If we break an oath that we have taken, we can bring a curse on ourselves, giving evil spirits right of entry to execute the curse on us.
Idle words/word curses (James 3:6,8; Mathew 12:35-37; 2 Timothy 2:16-17): Our words can be used powerfully for good or evil. They can be used to edify or destroy a person. Idle words can enact a curse on ourselves or those we've spoken to. Examples of idle words: "This job will be the death of me," "You'll never amount to anything in life," "I hope he rots in hell," "I'm bound to get cancer since it's in my family history." When a curse is spoken, demons are empowered to work according to what was said.
Satanic assignment: The Bible mentions instances where Satan asked for God's permission to oppress people (Job 2:1-7; Luke 22:31). If granted permission, Satan may assign his forces to work evil against a person.
Judgment: In some cases God may allow demons to afflict a person when they have failed to receive "the love of the truth" and/or have delighted in evil. 2 Thessalonians 2:10-12 describes this situation where God sends a powerful delusion on rebellious people so that they will believe the devil's lies. "Lying spirits" are the typical demons specializing in deception that may gain entry in this case.
Broken spiritual covering/being delivered to Satan: This can occur when a person leaves or is expelled from the body of Christ. When a church "delivers" a person to Satan, they withdraw fellowship and spiritual covering from the person in hopes that the person will repent from his sin and return to God (1 Corinthians 5:5; 1 Timothy 1:20). Once out of fellowship, the person is vulnerable to demonic attack targeting the flesh.
Broken faith: Since faith is our shield in spiritual warfare (Ephesians 6:16), any lack of faith could make us vulnerable to attack. With a weakened shield, Satan's darts may wound us, giving demons a foothold. Doubt is a common tool Satan uses to destroy faith and breed confusion (James 1:6-8).