A dedicated server is what it sounds like, a WHOLE server just for your site or sites.
If a website gets really large or busy it can need a tremendous amount of resources. In this situation, it would slow down other sites if they were on a shared or VPS server.
Dedicated hosting can be pricy however if your site is at the stage where a dedicated server is required we would assume it is also creating a significant income.
Not only do you have ALL the resources on a dedicated server there are other advantages such as being able to configure the server however you want it, not having other sites hogging resources, not being affected by bad mailing practices of other sites.