At the beginning, when first starting a website (or blog), everyone chooses the cheapest form of hosting available. It would be wasteful to pay for capacity you will not use, but there might come a time when growth will mean that you will not be able to sustain traffic levels on your existing package or even web host. Here is a list of packages and what you can expect from each:
This is what everyone starts with. Single digit charges per month that supposedly gives you unlimited bandwidth and diskspace until you become too big. Your site then gets suspended and the host will then point to a clause in the agreement that forces you to upgrade or change hosts. These packages are never really unlimited and are only meant as a starting point for a serious website.
VPS stands for virtual private server. What you get is a virtual machine on a physical server shared with other VPS clients. You get a guaranteed allocation of resources and are not sharing the server with thousands of other sites and users. This will also give you a taste of what its like to manage your own server and the power that comes with it.
When you outgrow a VPS, that is when you get your own dedicated server. This means exactly what it says. You get your own physical server hosted at the data center of your web host. Once you have a dedicated server, you can server a lot of visitors.
These define the basic categories of hosting you can expect to encounter as you grow. Once you get to the very top, you can purchase additional resources (servers) to meet demand and scale in realtime.