Why? Because word of mouth only gets you so far in the internet era. People discover new businesses—even local business—via Bing, Google, and Yahoo. The days when they'd just look you up in the yellow pages are long gone. If you don't have a sharable website address, your chances of building online word of mouth via social networking plummet, too. In other words, no website, no discoverability, no money. Of course, web hosting isn't just for businesses. You may want to host a personal website or blog, too. Either way, the services here have you covered.
A VPS runs its own copy of an operating system (OS), and customers may have superuser-level access to that operating system instance, so they can install almost any software that runs on that OS. For many purposes they are functionally equivalent to a dedicated physical server, and being software-defined, are able to be much more easily created and configured. They are priced much lower than an equivalent physical server. However, as they share the underlying physical hardware with other VPSes, performance may be lower, depending on the workload of any other executing virtual machines.