To keep the site up to date and relevant: In order to maintain credibility with your customers, you need to be able to provide them with reliable and up to date information; e.g. product description, photos and prices. It is vitally important that services that are no longer offered or discontinued products be taken off your site as soon as possible.
To keep the site fresh: As is the case with many aspects of modern life, websites are subject to fashion trends and developments in technology, particularly. For example, as internet connection speeds have increased in recent years, the use of bandwidth hungry web page elements such as "Flash" animations (video), audio and extensive still graphics has increased significantly. In order to keep up with your competition and take advantage of the latest in technology, it is a good idea to consider a "makeover" for your site on an annual basis. It is in your interest that customers find their visit to your site to be a satisfying and suitably pleasurable one.
To continue to be noticed: Everybody wants a high ranking in search engine results. Unfortunately, unscrupulous web developers constantly look for ways to provide their sites with an unfair advantage. This forces search engines such as Google, Yahoo etc to respond by constantly amending the algorithms controlling search outcomes in an effort to maintain fairness. This means that what constitutes valid search engine optimisation today, may be out of date in six months.
So, in a nutshell, website maintenance ensures that your site continues to do its job in the months and years following its creation. Your website is like a car, house etc; if it is not properly maintained it won't perform and will become stale.