Dedicated server web hosting is not as common as shared web hosting because most people don't have the need for dedicated servers. Large businesses are the best candidate for dedicated servers as well as web hosts. What is important to understand is that "shared" servers can actually mean that one server is split up for up to 200,000 customers. Not all shared servers have this many sites on one server but it is possible and when it gets too overloaded things can run slowly and be unreliable. This is why shared hosting is not the best idea for businesses online. You need reliable hosting that has great capabilities for growth and to have the power to keep your customers happy.
When you have a dedicated server you don't share the power or that server with anyone else. This means that things are more reliable and that your pages will load fast and process information more efficiently.
Some very good reasons to go with a dedicated server are if you are running multiple MySQL databases or PHP, if you run forums, if you have an ecommerce site that has shopping cart capabilities and you have enough sales to warrant it, and any sites that require specific configurations.