Initally labelled a 'Google Killer' it is nothing of the sort. What Google does - very well - is make it easy to search through as much of the world wide web as possible for specific search terms. What Wolfram Alpha does is make information computable. But what does that actually mean?
It means that Woolfram Alpha is building up resources of data that can have calculations run against it. This means that whilst Google can tell you every single page it has found where the number 1970 appears (http://www.google.co.uk/search?hl=en&q=1970), Wolfram Alpha will recognise it as; an integer, a year, an even number, etc.)
However, Google can also do basic mathematics (e.g. if we type 1970 - 1960 into both, they give the correct value of 10), but will struggle when things get more complex (e.g. typing 1970-1960x into WA will actually plot you the value of 'x' http://www.wolframalpha.com/input/?i=1970-1960x)
So is this a cuase for concern for Google? Well not really, despite there being a lot made of the alledged rivalry between the two) as Google has its own version of Wolfram Alpha up its sleeve in the form of Google Squared, a product from its labs project that it showed off last month.
If you type in 'Google Squared' into Wolfram Alpha, rather than get a long mathematical answer to a very large number multiplied by itself, you get the message:
"Wolfram Alpha isn't sure what to do with your input."Ooooh... Nice touch!