A static website or sometimes called hard coded is one that does not have a content management system attached to it and changes can only be made to the site via the code. Normally you will need a programmer to make changes for you unless you are fluent with the coding languages that it uses.
Many smaller companies or companies that opt for a cheaper website go for a static one as they are normally not as expensive to set up. If you have a website that will require frequent changes being made to it then a static website is not normally cost effective as most programmers will charge you for every change you need making to the site.
There are a few good CMS systems out there and many web development companies have now built their own to allow complete flexibility by being able to add the majority of things a customer may require on their site.