The concept behind the "Foveon" is rather simple. Regular image sensors capture all light pretty much indiscriminately -- no matter what color. What makes it work is that they add color filters on top of each pixel. A "red" pixel grabs red light by throwing away any blue or green light that hits it. Effectively, you are throwing away 1/3 of the light using those filters.
Foveon sensors, on the other hand, work quite a bit differently. It takes advantage of the fact that different colors of light can penetrate the silicon differently. Red light goes through silicon better, so it will tend to go deeper. Blue will pretty much stop at the surface. So, each pixel captures ALL of the light that hits it, and the color is detected by how deep the photon goes.
This means that, all things being equal, a Foveon sensor will work just at well using 1/3 less light. Also, without the filters, you will have less of the moire patterns that regular sensors give you. The image results also feature an apparent resolution approximately three times better.
Really, I do not know why this type of sensor did not become more popular. The only down side that I can think of is that I expect that the sensor is significantly more expensive to make due to the 3D nature of getting different regions embedded at different depths in the silicon. That, and patents...