The short answer is that 64-bit DP is analogous to entering all values to the penny in your tax return and not rounding to dollars until you've calculated the final sum vs. rounding each value to the dollar when you enter it, and adding the rounded values.
With the higher resolution, $100.51+100.51 becomes $201. Without it, you get $202. 64-bit DP gives a more accurate sum when adding a bunch of 32-bit sample values and then fitting the result back into a 32-bit range.
It's questionable how audible this is in the real world, but mathematically it's more precise; a penny saved is a penny earned.