SaaS is a new buzzword and every one is talking about it.
SaaS Stands for Software as a Service; this means now you can consume software as service and need not own this as per earlier licensing policy.
Let's see few examples to understand this better
Today we do not own mobile phone network or for that matter cable TV channels, we consume this, we pay a monthly rental and consume it. The service providers or operators gives us various plans/schemes from which we can select the one that is most suitable. One can choose or change the plan as per their convenience and need not stick to it for lifetime. You can also terminate the service whenever required.
Let's take an software example
You invested in MS win95 and bought few licenses for your business. Now you own them by paying an higher cost but now without the upgrade and support you cannot use this software as other business application would not support the older version of OS (operating system).
Hence you need to upgrade to the latest version of windows operating system say Vista or Windows 7.
Software as a service gives the advantage to the consumer by saving the higher cost of owning the software and but also gives you free support and version upgrades during subscription period.
Scaling up and down
As a service you can scale up (during uptimes) and scale down (during recessions) thus give you the control on per month cost and long term saving.
Pay for what you consume
You only pay for what you use and need not plan for life.
Software installed on your server
If you have infrastructure ready, why not use the same. You can save a lot on the software cost as you only subscribe to the software. Some businesses even have mandate to keep data within there network and not on the hosted or service provider server.