A domain redirect is an instance where a visitor who attempts to access a site or site content under one domain is sent to a different domain. Depending on how the redirect is configured, they may be sent to the same or similar content on the other domain, or they may be sent to the root (top level) of the other domain. This can be useful if a page has permanently moved and it is known that a large number of users may have bookmarked that page. When moving content from an old "site" (former domain) to a new site or new domain, redirection is strongly encouraged to avoid losing search engine rankings. The search engines periodically check all the content in their index, and if the redirect is set up properly, it will guide the search engine to the new domain and at the same time alert the search engine to update its index.
A redirect can also be from one file or directory to another on the same domain. An example of this type of redirect would be if you have a file named page1.htm and move that file to page2.htm. You could create a redirect such that all visitors trying to access the page1.htm page would be automatically redirected to the page2.htm page.