Essentially it is a process used to precipitate tartaric acid from the wine. If you have ever baked you might have used cream of tarter, which is the by product of wine making. To cold stabilize chill your tank, carboy or other container to just above freezing to precipitate the acid crystal out of solution. These crystals, when found in bottles are typically referred to as wine diamonds. They are harmless. For home production, you do not really need to cold precip unless you plan on giving wine away as presents. The crystals are more visible in whites and really are just a visual issue.
Tom