Quench, or squish area is typically the flat area on the top of the piston that's almost level with the top of the block deck. It must have a corresponding flat area on the deck surface of the head to qualify as quench.
If you look at a combustion chamber, you will usually see these flat areas, and they will have the volume of the actual combustion chamber between them. When the piston is compressing the mixture, as the piston nears the head, the flat areas on the head and piston come together and force the mixture from those areas to "squish" into the chamber, where the spark plug and burning mixture reside, so you achieve a more complete burn.
The quench area also runs cooler than the rest of the chamber / piston. These lower temperatures are where the "quench" comes from.
When properly designed, the quench areas can have a tremendous effect on the quality of combustion, and allow higher compression ratios, and due to this they are considered "artificial octane" by scientific types.
Bottom line is "properly designed, quench is good".
