There are many advantages to a dedicated server over other forms of a hosting account which is why it makes sense for businesses to choose dedicated servers as opposed to other server types for better performance, efficiency and reliability. If you would like to select a hosting platform for your powerful website that may be running powerful scripts which may get thousands of simultaneous visitors each of whom may want to be running a local version of the script, you will have to go for a dedicated server that is powerful enough to handle multi tasking.
The more your usage demands, the better power your hosting needs may demand. This is because you cannot afford going for a hosting account that crashes when multiple visitors try to execute scripts simultaneously. This is a common problem with shared hosting accounts or even for virtual private servers as suggested by Startups Genius which is why your web hosts may impose restrictions upon you on what you can and what you cannot do with your basic hosting account. The more power you require, the better hosting specifications you may call for and the more money you can expect to have to pay to manage such a server. Things could get costly for you which is why you need to be proceeding with care.