The development of automated and connected driving functions is currently a central objective for vehicle manufacturers. Such functions generally are introduced at different levels of automation with limited operational design domains (ODDs), which is gradually extended. However, a concise and practical description of ODDs has not yet been established. This work aims at providing a suitable and mathematically concise description of the operational design domain and relates the new description to the definitions of related terms that are widely used in the research community. This work follows a top-down approach. Engineering applications for ODD descriptions are introduced that go beyond scenario-based test design, like ADAS specification, function delimitation and cooperative, connected mobility. Furthermore the ODD can be seen as an instrument and language for the description of system capabilities, building a fundamental tool for cooperative and collaborative development and operations. A set of requirements on the parameterization of operational design domains is derived and methods for selecting suitable parameters are presented. The application of these methods is demonstrated with real world examples. Finally, a discussion of open issues provides starting points for continuous further research.