The Oracle database is comprised of the physical files on disk. When the instance terminates, it is these files that make your data persist across shutdowns.
Normally, only one instance can attach to one database. If you are running Oracle's Real Application Clusters, multiple instances can attach to one database for high performance and high availability.
These concepts are discussed fully in the Oracle Concepts Guide. Please go to http://tahiti.oracle.com and click on your Oracle version. Then read the Oracle Concepts Guide for more information.