ill try to explain it really simply.
1. firstly, you must know that electrons of an element will only absorb specific wavelengths of light.
2. Now, in the AAS LAMP, a light containing the element to be analysed is shone. this results in it producing a specific wavelength of light.
3. Next, another seperate flame vaporizes the SAMPLE TO BE ANALYSED. Many people are confused at this part because they think the vaporized sample is the same as the flame. IT IS NOT.
4. As the sample to be analysed is vaporized, the light from the OTHER lamp will is shone on the vaporized sample. some of the light is absorbed by the vaporized sample, due to the element to be analysed being present.
5. the concentration of the element in the sample is proportional to the amount of absorption of the specific wavelength (this is picked up by a photomultiplier and then a detector)
hope this clears it up. i know its a bit long, but i tried