The Greek word gnosis refers to either a "seeking to know", or (more commonly) to knowledge or wisdom itself. It's a fairly common word; I counted 29 uses in the New Testament and at least 60 in the Septuagint. Exact meaning derives at least somewhat from context.
Gnosticism comes from the Greek adjective gnostikos or "good at knowing; learned; sagacious". There are a lot of flavors and variations, and the term can get mis-applied. But I believe one of the common cornerstones of gnostic belief is a duality between the material world and the upper/spiritual world, with the goal of the gnostic being to transcend the former to attain the latter through the realization of "gnosis" - meaning, in their tradition, esoteric or spiritual/intuitive knowledge.
I've heard that the reference in I Timothy 6:20 to "the contradictions of what is falsely called knowledge" (i.e., gnosis) is a reference to a very early form of gnosticism. But I have no idea whether that's accurate or not.