Stephen Wolfram wrote a great blog post in January 2011 comparing IBM Watson with Wolfram|Alpha side by side, entitled “Jeopardy, IBM, and Wolfram|Alpha”.
Apparently Wolfram|Alpha uses Stephen Wolfram’s own Mathematica software to supposedly compute symbolic representations.
I would welcome a more detailed explanation of just how this works myself! ;^)
I was able to find this Youku video of Stephen Wolfram’s brother Conrad Wolfram explaining symbolic computation in Mathematica.