PaaS, as Wikipedia puts it, is a bit clumsy to understand. You can get an expensive definition with examples from Forrester, if you will :) There is also the platformasaservice.com which seems to be (or to become) the central place for PaaS related resources. Also Google Search gives some useful links to read about PaaS, worth checking at least the first ten of them.
Why am I writing about PaaS? Because I got excited by the term, which I never heard or thought about.
Before not long ago I new SaaS, which currently is quite a comon business model - simply put up some software on your infrastructure and charge the users for using it. The best example in this area for me still is CRM provided by SalesForce.com. At Optaros we call this model Rent. You can read about Assemble vs. Build, Buy, Rent in the company's blog, pretty simple and quite interesting.
So SaaS is an genious idea. It allows for recurrent income, which is always good in hard and unpredictable times (provided that the customers are already there). Optaros realized that Assemble goes very well with SaaS in the way that we call Hybrid offering. To keep it simple the hybrid offering is: build the app and rent it (most likely to the same customer). Doesn't it sound more like a nice theory which is practically difficult to implement? Well, it is difficult but not impossible. Just check out what the Assembled Web is and then combine it with OView. Shortly, customers get a bunch of assembled apps floating around the Web and delivering their branded presence outside their main Web site. Moreover the customers get full control and overview over theoe apps. So this hybrid offering is really a simplified PaaS.
Having said that, looks like PaaS is actually a natural successor of SaaS. Intuitively it's something more than SaaS. What constitutes "more" is the delta between what is Software and what is Platform. Hence in PaaS business model it's a more complex software that's being rented. The complexity varies. It can be a virtual machine(s) that you rent, e.g. Amazon Elastic Compute Cloud, Google Apps Engine, etc. or infrastructure to build apps there, e.g. Bungee Connect, SalesForce.com, etc.
Interesting what goes next in the line of SaaS > PaaS > ???. Soon my laptop will contain no code, nor IDE... just a browser. And I will forget how JAVA looks like, what is PHP, what is scalability issues, etc. I will just program on REST APIs and buy resources from someone on the cloud. Sounds like fun.