When a search engine or user looks for a previous url they are redirected to the new site.

This is useful for two main reasons:

Firstly if you have built a new website or have a new domain you want the site to be held on, you can use a 301 redirect to keep all the good SEO work that you have already done (especially the incoming links)

Secondly you can alter the way search engines look at your own url variations. As an example search engines may think www.blogyourworld and blogyourworld.com (no ‘www’) are two different sites. Once a permanent 301 redirect has been put in place search engines will know that any links pointing at www.blogyourworld.com are also pointing at http://blogyourworld.com .

By correctly configuring a permanent 301 redirect, you rankings will most probably improve as all inbound links are correctly counted for the website.
I have implemented a 301 for my blog. So if you type either www.blogyourworld.com the web browser will always show http://blogyourworld.com

If you are not sure how to implement a 301 then contact your web host, generally it is a very simple exercise and they should be able to do it with a mimimum of fuss.

Incidentally, ‘URL’ stands for Universal Resource Locator’, but I’m sure you knew that already.
Thanks!
Mark