Privacy, power and control.
Aside from the incredible capabilities of a dedicated server, there are plenty of other advantages associated with having a dedicated hosting plan. Most dedicated hosting plans come with multiple IP addresses, allowing you to place different websites on their own IP addresses, rather than sharing an IP address with hundreds of other website owners.
You also have complete control over the server's software configuration, which means you have the freedom to use any server-side application you'd like. In comparison to shared hosting plans that have unchangeable software configurations, the freedom of a dedicated hosting plan is far more desirable.
With a dedicated web server, you can push your site to the limits, adding thousands of pages of content and experiencing unlimited traffic levels with fast loading pages and almost no site downtime.