If you currently have a website but are going to be making some major changes to it then you have a few options. You can, of course, make the changes straight on to the live site but this is often not recommended as if something goes wrong you may end up bringing your whole site offline. Also if your viewers visit the site as you are making the changes it can be quite worrying for them to see it suddenly change or they may find it crashes whilst they are on it.
The best way to make changes on a site is to have a development test site that you can work on. You can then check everything is working thoroughly before you swap it over on to the live site. You can also then allow your client t see a fully working version of the site allowing them to check it over and make changes before it goes live to the rest of the world.
When making any changes to a site it is vital to have a recent back up so you can revert back to it quickly should you need to.