Greenhouse gases and saturated wavelengths?

I have seen people state that the relationship between greenhouse gases and certain wavelengths is logarithmic and up to the point of saturation will continue trapping more heat. After saturation is reached I have heard that there is very little warming that can be attributable to the gases that absorb at that wavelength. I do not quite understand saturation as of yet though. I have read that once a band is saturated the warming attributable to those gases will increase in altitude and nothing will ever truly be saturated to a point where no energy will be absorbed and no heat produced. Can someone clarify exactly what saturation means? Why is CO2 said to be saturated at the center of it's absorption band? And, as a side question, why have I read that higher altitude warming due to CO2 is more important than lower altitude warming?