"Root" gives you administrative level access to edit, install and configure all of the files on your server, including system-critical files. It gives you ultimate access to your server. This gives you the ability to configure your server to your exact needs. While root access gives you full control of your server, it is intended for experienced users, engineers and developers. That's because you do have the potential to misconfigure or delete those system critial files if you're unfamiliar or inexperienced with what you're doing.
VPS hosting is like you are living in an apartment complex. It means that other people are living in the same building, but you have your own secure apartment. You will get more room and restrictions will be fewer as compared to living in a dorm. It also means that if your neighbour is misbehaving, it is the problem of owner of building, not yours.
Dedicated server hardware is also limited to a single tenant usage whereas VPS hardware is shared by multiple hosting customers on one partitioned web server. The latest trends in web hosting have seen companies move beyond the single server model on cloud, VPS, & shared platforms to host multiple copies of a website's files and use network load balancing software to route traffic to the hardware with the most open processing capacity for better response times.

Think of a shared server as a large apartment complex, and all of the individual apartments are rented by other website owners. All of you need a place to live — just like your website’s files — but going out to buy a huge family home would be too expensive for your needs. Sharing common areas and utilities in an apartment block helps keep costs down. And the same is true for shared hosting.

Of course, one of the most important factors in selecting a VPS is the cost attached to it. VPS providers will charge more for managed hosting and for using high end resources. Hence, you need to select a VPS which will not only operate effectively, but will also not cause a sizeable hole in your wallet.
As you can see, a VPS can be the perfect middle ground for many – enough flexibility and resources for those who need more access or control than on a shared server but without the cost of a dedicated server. If you need root access, you can’t get that on a shared server, but you can get it on a VPS. If your site experiences unpredictable swings memory usage, and your host provides it, then the presence of burstable memory will be attractive. And, if you’re a fan of customization, then the fact that you can customize server-level software such as PHP, MySQL, and Apache will perk your interest.  In short, choosing a VPS will allow you to have many of the same characteristics of a dedicated server but in a more affordable and manageable package.