When you sign up for a web hosting company to put your site on their server you are typically looking at a very low price (under $20 per month and sometimes under $5 per month) and in these cases the web hosting company is actually not using a dedicated server for your site.  If they were then they would be out of business very soon.  The fact is that in this situation you are signing up for shared hosting and that means that your website might me one of dozens or even hundreds of other web sites hosted on that same server.  The advantages of this of course is the price.  You could never get a dedicated server for the same price (they typically run over $100 per month for the bare bones package and can run into the thousands per month).  The disadvantages are more numerous.  On a Shared Hosting plan you cannot install any software that isn't already part of the package, you might be sharing the same IP address as many other sites and the server is distinguishing requests by address once they arrive at the server, and most importantly if someone on the same server as you compromises the server with their web application (in the case of dynamic code) then your site is going to be dragged down too.

This isn't an attempt to completely scare you off of Shared Hosting solutions, but be warned about the disadvantages before you jump at the price.  I use shared hosting of simple sites that I consider low security, for everything else I go Dedicated Server all the way.