Oracle Database is a relational database system and the core of Oracle's business. The current release is called Oracle AI Database 26ai, following 23ai. Organisations either install it on their own servers, for example on Linux, or use it as a managed service through Oracle Cloud, including the Autonomous Database. According to Wikipedia, the database is also available on Microsoft Azure, AWS and Google Cloud.
Oracle Corporation is headquartered in Austin, Texas, and the software is proprietary. When self-hosted, data stays on infrastructure the organisation controls. For the cloud, Oracle offers its EU Sovereign Cloud in Frankfurt and Madrid, which Oracle says is operated exclusively by EU personnel and is physically separated from the public Oracle Cloud; trade press noted that these promises had not yet been independently verified. Oracle remains a US company, so US jurisdiction, including the CLOUD Act, remains a point of attention for a European organisation.