If your website has a long URL (web address) as a result of being hosted on a free web host, these free services provide you with either a free subdomain name or at least a shorter URL that you can publicize on your website. When visitors enter that shorter URL, they will be redirected to your actual website. Unless specified otherwise here, you may assume that the free services impose some sort of advertising on your site, whether a popup window, banner frame, text link requirement, or otherwise. Note also that some of the services listed below provide DNS services as well, and allow the subdomain name you sign up for to be directed to an IP address.
In general, URL redirection services are meant for people who host on free web hosts or on their own ISPs. Where possible, particularly if you want a permanent URL for your site that does not disappear, you should get your own domain name. It's so cheap that, unless you have no income at all, you can even get one for your personal web site, etc. You may also want to read my article Tips on Choosing a Good Domain Name. A step by step guide can be found in the article How to Register Your Own Domain Name.
Explanation of Some Terms Used in URL Forwarding
"Path forwarding" means that if your visitor enters a filename together with the shorter URL (like www.whatever.com/somename.html) they will be redirected correctly to the somename.html on your actual URL. This is not automatic for all free web redirection services.
"URL Cloaking", "Stealth / Cloaked URLs" or "Masked URLs" means that your visitors will not see your actual web address (URL) when they arrive on your site. This is typically accomplished by putting your website in a frame.
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