Wolfram Alpha is a different type of search engine, and has been written about a lot. Unlike Google, instead of links it gives you data, figures and graphs abut your query.
While alone Wolfram Alpha feels a bit limited, but with Wolfram Alpha Google, results from both search engines are combined giving you the advantages of both. This Firefox add-on barely changes your browser - just adds a little icon to the bottom and a button to the Google search page.
When you type in your query, Google is much faster, but after a couple of seconds it will be joined by Wolframs' results. There are some things Wolfram does very well, like geographical questions or statistics, and it's nice to have this available so easily.
For many queries, the Wolfram side of Wolfram Alpha Google will not respond, as Wolfram is much smaller than Google. The slowness of response is also a pain. Nevertheless, if you're a fan of Wolfram, this is a great way to use it.
With smooth integration, and sometimes genuinely improved search results, Wolfram Alpha Google is a useful addition to your web experience.