URL redirection or URL forwarding is basically when a website tells a browser that a page has moved. For example, the page formerly hosted at http://OldURL.com may now be at http://NewURL.com. Thus, as the webmaster you'd want to tell anyone that goes to OldURL what the new address is - something you can do automatically via a browser redirect (http status code starting with a 3)
There are two most common types of redirects, a 301 redirect and a 302 redirect. A 301 redirect means that a page has been moved permanently while a 302 redirect means that a page has been moved temporarily (or for an unknown reason).
If your page is moving to a new URL for whatever reason, and you want to maintain the SEO authority that you've built up (e.g., from multiple inbound links pointing to the old URL), you'll want to use a 301 redirect. The 301 redirect tells search engines that whatever authority they were previously ascribing to the old URL should now be passed on to the new URL, and therefore you shouldn't lose any of your SEO authority.
That said, there have been occasions where people have attempted to use redirects to game search engines. For example, one could buy another site with a good deal of inbound links and then attempt to 301 redirect that site to your site and transfer its link credit. Search engines can often spot these maneuvers and will see through them, thus removing the inbound link credit. If you're going to purchase a site and want to maintain its credibility make sure to thread carefully and read up about best practices prior to doing it.