Culinary definition of clarify: To remove cloudiness or particles from liquids - ie: stocks, etc.
C@H FOOD FOR THOUGHT
There are some very sophisticated and time-consuming techniques for clarifying stocks, broths and liquids by using raw egg whites and food acids, but unless you are cooking in a restaurant or serving the Queen, good old fashioned repeated-skimming, cheesecloth or coffee filter straining, or cooling and skimming, will do the trick quite well. A final pour through cloth will clear things up quite well, but if you have time to let things cool and settle out before pouring off the clearest liquid at the top, you should end up with a very clear stock to re-heat.
Clarified butter is easy to make and stores well. Slowly melt whole butter over low heat and continually skim floating solids from the surface. Then, cool the remains slightly until heavier particles settle to the bottom, and pour off the 'middle' or so layer of clarified butter. Discard the solids and store the clarified butter in an airtight container in the fridge for a month or so.
Unclarified (straight out of the wrapper) butter burns easily (the milk solids do, at about 250F), but clarified butter does not, so for many applications, chefs prefer the latter.