What is considered Gnosticism (within the context of Christianity)? My background is not religion, it's closer to philosophy, so I lack necessary context. Gnosticism translates to 'knowledge', so what is it a Gnostic 'knows'? What is an example of Gnosticism or Gnostic arguments?
The key difference between orthodox Christianity and gnostic Christianity was that the orthodox required faith in what was taught by the elders, as received (or, if you like, supposedly received) from the apostles. In order to ensure uniformity, orthodox Christianity developed a hierarchy, so that bishops could oversee presbyters, who oversaw deacons, all passing on the same gospel message. 

Gnostic Christianity had no need for bishops, because gnostic Christians were permitted to seek knowledge by revelation. If a member received, in a dream or otherwise, new knowledge (gnosis) then he or she could tell others in his community. If it was widely accepted, the community might adopt it, resulting in an evolution in belief. If only some members in the community accepted the new knowledge, it might result in a breakaway movement, something which occurred from time to time and generally without acrimony. At its peak, it is suggested that around half of all Christians were gnostics.

As you could guess from the above, there was no one Gnostic belief, and it would be too broad to summarise them all. What gnostic groups tended to believe in common was that the Old Testament Creator God, whom they called the Demiurge, was a different God to the more loving New Testament God. Sophia, the Lady Wisdom of Proverbs and other Jewish wisdom literature generally played a key part in gnostic theology. Gnostics were discouraged from bringing children into this evil world, to suffer here. 'Light', which we see mentioned frequently in John's Gospel in reference to Jesus, was an important motif. Most gnostics were vegetarians, because they knew that vegetables contain light, and melons were favoured because they contain more light. 

The earliest known gnostic gospel was the sayings Gospel of Thomas, now generally believed to have been written in the middle of the first century.