Leaving your beer on the yeast cake for a brief amount of time after the primary fermentation can be useful. Yeasts produce some precursor alcohols during early fermentation while they are consuming all of those malt sugars. These include "off" flavor sources such as acetylaldehyde and diacetyl. By letting the beer rest on the yeast cake for an additional week after fermentation has ended, the remaining yeast will turn on these early alcohols and convert them, eliminating the off flavors. This is known as a diacetyl rest.
Beer is a living thing. Some beers are meant to be consumed young, such as IPA's or hop forward beer styles. Hops begin fading the moment they are used in your beer, and a fresh hopped ale isn't the same beer at all six months down the road. Other beers, such as high gravity barleywines, old ales and others benefit from a long time in the bottle. These beers can be quite bitter and tend to mellow out and mature in flavor once they've conditioned for a long time (greater than six months). They'll develop complex flavors on their slow, gradual decay into vinegar. Usually, the higher the alcohol the beer, the more "Cellerable" it's considered. The higher alcohol content helps retard the slow gradual decline of the beer and several beers can be kept for years in a cool, dark, dry environment (if not decades).
