Well, I tried to explain that the response over time gives a collection of points that can describe a curve. You can integrate that curve, geometrically or by using calculus, you get an area. We typically describe the area as the response, in chromatographic determinations. And the Latex is appearing for me now, so I see you're describing the ratios of your two areas. Of course, like DrCMS: said, your areas are useless for quantitation, unless you have run a standard first. Or you have been given a calibration factor, like DrCMS: told you, which lets you know the corresponding responses of the two compounds on a TCD.
You keep being very abstract, asking "what does this mean" and "how does this work." So I'd like to ask you what answer do you need to give, and what pieces are you missing that prevent you from figuring the answer out. I'm sorry you can't get the "meaning of area number" from how the TCD detector works, but the detectors responce, by the change in thermal conductivity of the flowing carrier gas, over time, is exactly where the area comes from.