Just as a VPS is efficient in it's use of resources, it is easy to upgrade or downsize your hosting resource limits. A number of businesses find this useful in order to have the resources for their peak season and then be able to downgrade during their off-season.
One thing a dedicated server does is provide root access, while shared hosting does not. A VPS however does give you root capabilities, while costing a lot less.
A VPS plan is far more cost efficient than a dedicated host, especially for new sites. When you buy a VPS server, the plan is tailored towards your expected resource usage, as opposed to paying for a dedicated host and extra resources and money away each month.
Beyond the fact that it is less money, a virtual private server can be run on a virtual machine (as opposed to a dedicated server which is an entire computer being used for the means of hosting).
Setting up your virtual private server does not take long. In addition, you have the flexibility to configure them however you want (and with whatever operating system you want).