Local development is the concept where you install a full stack of server software on your personal computer. A local environment not only creates a sandbox where you can mess around with the site, but it will make the site much faster since there is no Internet access required to load the site. Note the later point may not be 100% true with modern sites. Nowadays there are things like Typekit, and many sites may be connected into various third party APIs required to run the site, for example Chargify. Make sure to setup an environment dedicated for local development in the case of such APIs whenever possible.