Crypto-as-a-service or cryptocurrency-as-a-service (CaaS) has not yet fully been defined. It can literally mean any sort of Software or Platform as a service related to the crypto world. In the broader sense, Crypto-as-a-Service is the ability to launch a crypto-related product/service, with the service provider providing not only the platform rails but also the regulatory (read: licensing) and compliance rails as well.
For example, if someone is trying to launch an OTC (Over-the-Counter) Bitcoin Trading Desk, then a CaaS (Cryptocurrency-as-a-Service) would imply that the solution provider is able to provide the platform rails (i.e. API), custody of funds handling, licensing, compliance, anti-money laundering, KYC/KYB, and reporting requirements at a very minimum.
This allows businesses who wish to build products and services to go to market quicker and be fully compliant with the local laws and regulations.