Shared hosting and VPS are two ways to rent server space on a web host, or company that rents out server space on which you can store your website. There are pros and cons to each method, and it's important to understand the differences before selecting one for your website.
When you use a shared hosting service, you're renting space on a server that is shared by other users. In some cases, all of the users of the server are on one account, and in others, several websites might be sharing one server. For example, if you have an up-and-coming blog that isn't getting much traffic yet, you might want to share hosting with another site or sites.
On the other hand, VPS stands for virtual private server. This means that you have your own space on a server that is not shared with others. The difference between shared hosting and VPS is very similar in concept to the difference between living in an apartment complex versus living in your own house. You still have neighbors (other websites), but they don't intrude on your space because you have a wall (a specific server) between them.
The most obvious difference between shared hosting and VPS is price: the cost of VPS hosting is more than that of shared hosting, but less than that of a dedicated server.