Demons were at one time righteous angels created by God. Lucifer, after he was given a throne of responsibility and oversight over one third of all the angelic beings (Isaiah 14:13, John 12:31, Revelation 12:3 - 4), turned himself into Satan the devil. After deceiving himself, he successfully deceived all those spirits under his responsibility. These spirits are the ones that became demons.
It is interesting to note that Jewish tradition assigns personal names to two spirits they believe are the most powerful demons. The king of all the devils is called Ashmodai or Sammael and the queen's name is Lilith.
Angels that sinned
The Greek word for angels means a messenger of God. It applies to angelic spirits but can also apply to human messengers like pastors. The word translated "sin" or "sinned" means someone who missed the mark of God's perfection or who has erred.
Kept not their first estate
Jude labels demons as those who did not keep their "first estate," meaning they rejected the initial state of righteousness God gave them.
Leviticus 17:7, Deuteronomy 32:17, 2Chronicles 11:15, Psalm 106:37
Matthew 4:24, 7:22, etc.
The Hebrew word translated "devils" in Leviticus 17:7 and 2Chronicles 11:15 refers to someone who is hairy or shaggy, with an illusion to the mythical beast known as a satyr (see the KJV version of Isaiah 13:21 and 34:14). In the two other Old Testament places where "devils" are named (Deuteronomy 32:17, Psalm 106:37), the Hebrew means a malignant spirit or demon.
Judges 9:23, 1Samuel 16:14 - 23, 18:10, 19:9, etc.
Luke 7:21, 8:2, Acts 19:12 - 17, etc.
Leviticus 19:31, 20:6, Deuteronomy 18:11, 1Samuel 28:9, etc.
Familiar spirits are demons who can be summoned by a variety of names to provide (or pretend to) supernatural services (predicting the future, contacting the dead, etc.) to humans. The witch of Endor summoned a familiar spirit for King Saul in his foolish attempt to contact Samuel from the grave.
A foul spirit is one which is especially unclean, impure and lewd.
Gods whom they knew not
Deuteronomy's reference is to pagan deities (evil spirits) that Israel indulged into worshipping.
Mark 5:9, 15, Luke 8:30,
A legion was a body of Roman soldiers that numbered roughly 6,000 men. Legion, in these verses, is not used as a name or as a reference to an exact number. It is rather a name used to convey that many demons had possessed a single person.
1Kings 22:22 - 23, 2Chronicles 18:21 - 22
Power of darkness
Luke 22:53, Colossians 1:13
God, even though he cast the devil and his demons out of heaven, has yet to take away all the original power he gave them. They use this power to deceive humanity into carrying out their will of chaos, confusion and destruction. God is the only one who can deliver humanity from being ruled by the forces of evil.
Prince of the kingdom of Persia
An angel (possibly the one named Gabriel) was sent by God to Daniel the moment he began to pray for understanding. The angel, however, took three weeks to reach him due to his inability to combat a powerful and evil demonic force spiritually ruling over the Persian Empire!
When the angel completed his mission to Daniel he had to fight his way back to God's throne as well (Daniel 10:20)!
Rulers of the darkness of this world
God has decided to allow Satan the devil, and many of his demons, to rule over and deceive the world up to the time of Jesus' Second Coming.
Spirit of an unclean devil
Spirit that now works in children of disobedience
This phrase references the collective work of demons to lead all humans into sin and rebellion against God.
Spirits in prison who were disobedient
1Peter 3:19 - 20
These spirits in prison were demons who, in the days of Noah, were preached to by Jesus Christ (see 2Peter 2:4, Jude 6).
Spiritual wickedness in high places
God, even though he cast the devil and his demons out of heaven, has yet to completely take away the original power he gave them. He has also continued to allow them access to his throne ("high places").
Unclean (demons) spirits
Zechariah 13:2, Matthew 10:1, Mark 1:27, 3:11, Luke 4:36, Revelation 16:13, etc.