Caching is a feature of web browsers that stores certain elements of websites, such as images and scripts, so that the browser can quickly display the website without having to download all its components again. Clearing the cache means removing this stored data. Private browsing is a mode that does not save the user's activities on the computer, and it is unrelated to the storage of website elements for faster loading. Proxy settings are configurations that allow a browser to connect to the internet through another server, which doesn't inherently affect how quickly a site loads from local storage.