The “aaS” letters usually mean “as a service”. For instance, SaaS means “Software as a Service”.
In that specific case, the idea is that instead of selling a specific version of a piece of software on a disc or as a download, the vendor keeps control of the software and you pay a recurring subscription fee.
The problem from the vendor’s point of view is that they release a new version every year or two but people won’t pay for the upgrade until they are forced to. Meanwhile, the user balks at paying a lump sum of $200 (or hugely more) to upgrade every year or two.
The solution from the vendor’s point of view is to sell the software as a subscription service. The user pays a smaller, more palatable recurring fee and the vendor gets a constant revenue stream.
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