The H-K Project uses a specially-designed instrument to measure the amount of light from active magnetic regions in stars. This light comes from calcium atoms that have lost one electron each. The different wavelengths of light emitted by these atoms were labeled long ago. The "H" and "K" light gave this project its name. This light comes from the upper levels of the Sun near active magnetic regions that we can see, like sunspots. Other stars are too far away to see these features on their surfaces. Studying the relative strength of these two wavelengths of calcium light from distant stars similar to our Sun gives an indirect measure of the amount of surface activity on the stars -- "starspots". Using this method, astronomers have been able to follow cycles similar to the sunspot cycle that has been observed on the Sun for centuries.
What follows is a more technical description of the H-K Project.