A static site is one that is written in HTML only. Each page is a separate document and there is no database that it draws on. What this means functionally is that the only way to edit the site is to go into each page and edit the HTML – so you’d either have to do it yourself using a webpage editor like FrontPage or pay me to go in and edit the site each time you wanted something changed.
A dynamic site is written using more complex code and can do a lot more. For instance, I can make an area where you can log in and change various parts of the site, such as adding information or products. This is because each page is constructed based on the information in a database, and the information in that database can be changed via another interface.