OK, you have all seen the question before BUT let's make the challenge a little different this time. I want you to use the Feynman Method ! You have to explain it simply, preferably just text but one or 2 sketch diagrams may be OK (no complicated graphs with multiple colours please) and I am going to limit you to 150 words. Who fancies the challenge - make sure you don't leave out any of the important physics. This question is asking for an explanation of how something works. I am not interested in experimental evidence or proof, just a clear explanation that you can chat about to someone to help explain the physics behind it in as simple terms as possible. Like if your mate down the pub says, OK, tell me how this works then.
The answer can be explained very simply. The Oxygen and Nitrogen (the non trace gases) are mostly transparent to thermal wavelength of light that leave Earth's surface. CO2 in the air, can be compared to colored dye in water. It's not too difficult to imagine that water with 280 ppm red dye might be visibly lighter than water with 400 ppm of the same dye. The real answer is somewhat more complex as you need to look at different bands in the IR spectrum that get reflected by different trace gases, but that's the gist.
55 words under. :-)