WordPress redirects URLs that are re-written?

I notice something very strange today when I re-wrote a blog post URL for SEO purposes. When I clicked on a link to the page from the search results of Google, I was taken to the new URL. I clicked back an noticed that the URL in green below the title link and description was of the old URL. So how is it that I am directed to the new URL? Does WordpPress have some in-built redirection service when a URL is written?