SaaS stands for "Software as a Service". 

Software as a Serice (SaaS) is a sofware distribution method, where a company offers software, usable via a website browser, in return for a monthly/yearly fee.

Another way to explain it, is to give a real world example.

In the old days, we purchased MYOB for our accounting package. We installed the software from a CD-ROM onto our desktop computers and laptops. This method of delivery software delivery is most certainly not SaaS based.

Nowdays, we don't use MYOB desktop version anymore. All our accounting is done using Xero, which is a browser based accounting package. We don't need to install anything on our computers and we pay a monthly fee to use Xero.

Xero uses a SaaS model. We are paying Xero a monthly fee to use their service (in this case, their accounting software available in a web browser).

The advantages for us is that we dont need to upgrade any software on our desktops, we can access our accounts on any computer connected to the internet (home, work, mobile phone, iPad, laptop, etc).

Many companies that offer software are moving to a SaaS business model. It is proving to lower barriers-of-entry for customers and provides a relatively consistent income stream (providing customer churn remains low).