SAP HANA was designed to be a truly modern database platform, and as a result the answer is: all of the above. A modern database should be a database, platform and be available on-premise or in the cloud.
SAP has a large installed-base of on premise ERP customers, and the HANA platform supports their needs, especially the need for an enterprise-class database. Many of those customers are looking for an on-premise database to replace the traditional RDBMS.
The demanding needs of an in-memory database mean that SAP elected to sell SAP HANA as an appliance, and it comes pre-packaged by the major hardware vendors as a result.
However the future of business is moving into the cloud, and SAP HANA is available as Platform as a Service (PaaS) and Infrastructure as a Service (IaaS) with HANA Cloud Platform and Managed Cloud as a Service (McaaS) with secured HANA Enterprise Cloud and via 3rd party cloud vendors. Customers can also choose Hybrid deployment model that combines on premise and cloud. More details on this are available here.