It appears to be seeding a random number generator with your mouse movements.
The mouse move handler itself does something along the lines of the following:
var b = ((event.X << 16) + event.Y) * (new Date().getTime() % 1000000);
c = c * b % d;
if (previousMouseMoveHandler) previousMouseMoveHandler.call(arguments);
d is (screen.width * screen.width + screen.height) * 1000000, and c is a variable that starts out as 1.
All of this is wrapped in the scope of an anonymous function, which itself is immediately evaluated to return a function that is assigned to a property named “random”. That returned function looks something like this:
var b = c;
b += parseInt(hash.substr(0,20), 16);
hash = MD5(hash);
return b / (d + Math.pow(16, 20));
hash, BTW, is a variable that starts out as the MD5 hash of the page’s cookies, location, the new Date().getTime(), and Math.random().
(Note, of course, that Google may change the script returned at any time and hence invalidate this analysis)