SaaS is an acronym for "software as a service." The funny thing about that is the basic definition of software is using technology to automate something that was previously done by a person by hand, i.e. a service. Obviously plenty of software today is doing things that are impossible for people to do by hand even over an infinite time period, but if we go way way back to how it all started I think it's a functional definition.
For example let's look at Zendesk, in its basic form it is a customer support ticketing tool. Before tools like this, people would literally write tickets on paper and you'd have to employ someone to keep track of them, manage them and assign them to reps. Zendesk automated the creation, routing and tracking of these support tickets.
The nature of this tool is an ongoing service, so while software in its original incarnation was sold the same way a physical good is sold - a one time fee + maintenance - we have transitioned into a world that better reflects the value that the software is delivering to the customer.
So SaaS is simply software solutions sold as a subscription - monthly, annually, multi-year - and based on a set price, per seat, usage, etc.
There is still software that is not sold on a subscription basis and there are plenty of subscriptions that are not software.
The other element of software that's really critical to understanding the business model is the margin characteristics. Software, by definition, is almost infinitely scalable (especially if it's multi-tenant cloud-based software). The marginal costs associated with selling to an additional customer are usually negligible. These create some really awesome scaling and margin dynamics which are pretty unique to software. The scalability and the margins are some of the key factors that make SaaS companies so valuable. Low marginal costs are table stakes in SaaS.
While other businesses can benefit from the subscription business model, it doesn't necessarily mean they will operate the same way or get valued the same way.
I'll dive deeper into unit economics often in later posts.