This tool displays the HTTP status code, server name, date, etc when you enter an url and click on the check button. You should use it if you've changed website domain name, enabled HTTPS, changed URL structure, removed a page, etc. If the URL you enter in the text field is redirecting, it will display the destination URL.
It is important that you use the right redirect code. Failing to do so will confuse the search engines or force them to remove your page from its index.
Redirects are of two types, temporary and permanent. A temporary redirect throws HTTP status 302 code before redirecting to the target URL. It tells the search engine that the page they've requested if not available temporarily.
A permanent redirect will throw HTTP status 301 code. It tells Googlebot, Bingbot, etc that the page they want to access has been pulled off or the user has changed its URL permanently.
Apart from redirects, the tool will also make you aware of broken links by reporting a 404 error code (not found). If you've deleted a page and it is not reporting 404 error, you should check the web server configuration or the code that's handling redirects/errors. Visit Wikipedia to know more about HTTP status codes.