Could you explain to me what Gnosticism represented or still represents?

What did it represented in the Renaissance Era?

Gnostics believe that they have secret knowledge about God, humanity and the rest of the universe of which the general population was unaware.

The movement and its literature were essentially wiped out before the end of the 5Th century CE by Catholic heresy hunters and the Roman Army. Its beliefs are currently experiencing a rebirth throughout the world, triggered in part by the discovery of an ancient Gnostic library at Nag Hammadi, Egypt in the 1940s, and the finding of the Gospel of Judas at El Minya, Egypt, in the 1970s.

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What Kanga says is accurate.
The question is difficult to answer in full, because Gnostic sects varied quite a bit. Most of them believed that the Earth was created by an evil deity (isn't it obvious, due to the fact that there is so much evil in the world?), which some sects identified as Yahweh. Jesus was sent to rescue us from the grasp of Yahweh. This is, of course, pure heresy to orthodox Christians and Jews. Or, if the Earth wasn't created by an evil deity, matter itself was evil. Therefore, you had to escape it. This was in keeping with Neo-Platonic ideas about the soul being trapped in the body. Gnosticism seems to have been open to Buddhism, as the text "Thunder, Perfect Mind" is quite Buddhist.
Oddly, many Gnostic sects allowed women to be ordained and to preach. The Gnositc text "The Gospel of Mary" was important in this regard.
Gnosticism was suppressed, but not entirely. Many of the famous heretical movements in Christianity were inspired by the secret legacy of Gnosticism, including the Bogomils and the Cathars. The Cathars concentrated in southern France and were wiped out in the Albigensian Crusade, the first Crusade launched against other Christians. A good source for this is Barbara Tuchman's excellent history "A Calamitous Mirror: The Distant 14Th Century." Another excellent author is Elaine Pagels.

Gnostics believed they had special knowledge that few others had. And they thought that their "knowledge" entitled them to do pretty much as they pleased. They equated the mind (the source of all knowledge) as being equal to and one in the same as the spirit

Gnostics were considered heretics by Chirstians in the first century. I am not aware of any influence they had on the Renaissance.

Today Gnostic ideas show up in a lot of New Age thinking. In dealing with Gnostics today as in the first century it is important to remember they feel they have special knowledge no one else has but I can never get them to disclose where their special knowledge comes from.

This is a major flaw in my view for if the source of special knowledge is unknown how can we evaluate the credibility of their special knowledge.