Greg, we recently ran a series of posts explaining key concepts of the cloud, including SaaS, PaaS, and IaaS.
Generally speaking, SaaS refers to individual programs (think your accounting software, etc.) that you wouldn't download as software, but instead access remotely over the web off the vendor's servers. PaaS is the same concept, but extended a whole platform for running various programs on.
Wikipedia.org? Does a pretty good job of differentiating between the various service models.