Because color theory works on pretty much everyone, we can be sure that we all perceive the relative difference in colors the same way. But what green is is a figment of your consciousness. What you think color, sight, and all your other senses mean exists only in your mind. Not as a physical process in the brain, but purely as a part of whatever metaphysical process that results in consciousness.
A color is not a real, tangible thing. It's just the way your brain perceives light of a certain frequency. There is no way to describe what that experience is because there's no universal reference. You can't describe color to a blind man, after all.
The fact that we can't identify them with our current level of understanding of the workings of the brain is not very surprising - it is an extremely complex organ and our tools for understanding organs are very primitive in the grand scheme of things.
The mind is a level of abstraction up from the brain. The mind is what the brain does, not necessarily what it is. Consciousness of course relies on discrete physical reactions in the brain, but in the way that software relies on the discrete transistors in a CPU. Consciousness is the emergent behavior of the system. It exists more on an informational level than physical, even if it is a physical process.