Web maintenance is the business of keeping the online branch of your business up and running. Many websites require skilled programmers to develop it, and anything so sophisticated needs experts to look at it and contribute even more from time to time. All websites are works in progress, so to speak, and like any engine that website needs a qualified operator.
Very large websites, with many functioning components and enormous amounts of data to process every second, sometimes have a full-time staff dedicated to keeping it up and running. Consider services such as Yahoo or Facebook; they have dedicated staff that constantly monitors performance. If anything goes wrong, they are there to work at it instantly.
Most businesses do not have a network anywhere near as broad as a social network or search engine, but something with a hundred pages and embedded coding needs someone to look at it on a routine basis. Website maintenance services is a third-party vendor that checks out a website every now and then. Sometimes a site is left to run until a problem arises, and then the programmer is contacted.