Get a good understanding of how it works with this introduction screencast.
Unlike last year's launches of Cuil and Wikia Search i'm far more excited about WolframAlpha as they are focusing on a part of search that isn't currently serviced sufficiently. The more factual infosheet side rather than a method of redirection to other websites (which is what Google does).
For me, it could take over from Wikipedia for provision of immediate-response factual based information (i'm not suggesting it will usurp Wikipedia, just for those times i need straight facts).
Queries such as, "What's the GDP of Germany?" or "Where is the ISS at?". Neither questions i ask as often as i type in "BBC football" into Google mind.
Relevant web links
Web tool 'as important as Google' - BBC News