Simply put, AWSP allows you to do computation on Alexa's computers. Those computers have the internet itself (> 100TB) in local storage. Back in October, Alexa's AWIS (which Paul referred to) only allowed you to access the data, and not do computation.
Before: Similar to Google or Yahoo search API - you can do a search programmatically.
After: Now you can write a C function that processes every page of a search result - and run it on Amazon's / Alexa's boxes.
See the difference? Amazon is creating an open San Diego super-computer center where anyone can schedule jobs.
I think it's a big deal. We'll see how many people can meet the pretty high technical skill standards to start using it. I also think that even though access to the data, storage, compute time and bandwidth is all priced a $1 per unit, it could be a bit more expensive to do stuff than people might think.