In my opinion, platform as as service (PaaS) is the most innovative service model in cloud computing.
It is also the least well understood, and has the highest confusion factor.
One way to think of an important PaaS variant is as websites that are used by other software, rather than humans. So Twitter exposes a PaaS model for other applications (such as phone apps) to use. The technology to do that is called an API (application programming interface), and it turns Twitter into a software component that you can program. Hence the phrase: the programmable web.
Want to read more about this, and see some application examples? Have a look at this great presentation. (Note: only the first slide is in Dutch. API Koning is a homophone word play alluding to king of the Apes, or API’s in this case.)
For even more information look at Anne Helmond’s blog post on APIs.