What is a testing server?

Unless you work with server-side scripts like PHP, you don't need one.

A local testing Server is typically installed on your computer.  Some popular ones are Wamp (Win or Mac), Xampp (Win or Mac), Mamp or Mamp Pro (Mac only).

To define a local testing server in Dreamweaver, go to Site > Manage Sites.  See screenshots.

A testing server is a server on which you 'test' your application/website before you release it to the general public on your 'public facing' remote server.

A lot of developers set up a testing server environment on their local computer using XAMPP or MAMP if you're on a Mac. These are freely available packages to download which contain all the elements you need and they automate the testing server set up process. You can Google for them to find out more informatiom.

You only need a testing server if you intend to do something dynamic using a server side language like php, connecting to a database, etc

You could also use node.js if you do not want to use php but that requires you have the lastest stable version of node installed. That will provide you with a run-time server environment for front and back end javascript but you would still need some kind of back-end database if your going to store information.