This word comes from the Greek term gnosis (Strong's Concordance #G1108, translated as the word 'science' in the KJV version of 1Timothy 6:20) which means 'knowledge.' Christian Gnosticism had its earliest beginnings in the reformation of the Greek religion beginning back in the sixth and fifth centuries B.C. It did not become a significant religious and philosophical movement until around 100 A.D. in the Roman Empire.
Gnosticism believed that secret esoteric (which means only understood by a few) knowledge was the source for salvation. Only those considered special were to have it. This theory does not make any sense, since Christians are to proclaim the Gospel to everyone, even when the people hearing it do not accept it (see Matthew 28:18 - 20, Philippians 1:15 - 18, Romans 10:12 - 15).
In addition, some version of reincarnation or the transmigration of souls is involved in Gnosticism. This teaching is contrary to the Bible, which states the dead are dead (unconscious) and do not know anything which refutes the concept of an immortal soul. Eternal life is only gained through a resurrection (see Ecclesiastes 9:5 - 6, 10, 1Corinthians 15:16 - 19). We did not have any prior lives so life is a single one-way trip.
Those who believed this teaching were radical dualists, and thought matter was intrinsically evil and spirit good. This goes excessively far. The author C.S. Lewis observed that God likes matter since He created it. The flesh is only evil if we choose to violate God's law, such as concerning having sex outside of marriage.
All variations of Gnosticism had one central belief in common concerning the Bible. This belief was that the Old Testament was a revelation from one God while what is written in the New Testament is a revelation from a different God. The God of the Old Testament was evil since He created the world as per Genesis 1. No Christian could accept such views, since Jesus was the Creator God or God of the Old Testament (John 1:1 - 3, Ephesian 3:9).
Additionally, the Bible is clear that God is perfectly good with no 'darkness' or evil in him at all (1John 1:5). The New Testament builds upon the Old Testament's authority (2Timothy 3:16 - 17, 1Corinthians 10:4, 11), and so the two are not opposed to each other foundationally as those who supported this doctrine believed.
Although the subject of Gnosticism is large, this brief description will motivate you to look further and study deeper into this topic. Please see our series on the definition of Christian terms for information on other Biblical words.