The following statements are not from Microsoft or other they are only my opinion and experience.
The Common Data Service is a platform which is developed by Microsoft. The Common Data Service is also known as CDS. I will use in my the short form CDS.
In my opinion there are several descriptions for different business needs available.
The First description is that the CDS can be a platform to store Master Data because there is a database (called Common Data Model) included. In this database there are a lot of standard entities and also the possibility to build custom entities available.
The Second description is that the CDS can be a service to transfer data from one service or system to another. So the user have the possibility to use different systems with the same data. With CDS the possible mistakes in Data transferring are going down to zero because with the CDS no user has to copy data from one system to another because the CDS will do this work.
The Third description is that he CDS can be the basic database for new business solutions or business apps. The Apps can be build direct in the CDS or with PowerApps using the Common Data Model database.
The fourth description is that CDS can be a Data Warehouse in which you can store all data from the business processes to do analytics with PowerBi. There is directly PowerBI integration to the Common Data Database. In the Common Database you can also store data from collecting services like Microsoft Flow.