VPS stands for Virtual private server and as the name suggests, refers to a vitual server which is dedicated for use by only one individual customer.
VPS hosting has several advantages over shared web hosting in the sense that customers have more privacy and normally dedicated bandwidth. Moreover, even though customers are sharing the physical resources, due to the nature of VPS, customers have more freedom to install apps and other software on their server. Plus it is cheaper than a dedicated and sperate physical hosting service in case you are unable to afford one.
If you do decide to go for VPS hosting, you should be aware of the disadvantages and the issues involved. In most cases you would be responsible for updating your software and taking security measures. Also be aware of the limits so that you do not end up overloading your VPS.