According to About Food, the aging process for meat begins approximately at 11 days, and should be watched carefully if left to continue past the first signs of aging. It must be kept at specific temperatures to promote the aging process.
One form of aging beef is called dry aging, in which the beef is left to hang in a controlled environment between 32 and 36 degrees Fahrenheit. Humidity is also required to combat natural water loss. Beef must be kept cold enough so it does not spoil and warm enough that the aging process can proceed. Aging beef causes enzymes in the meat to break down connective tissues and evaporate water content, concentrating the flavor of the meat.