In computer science, a core concern is one of the main features or concerns a program is written for.
Example:
If writing an application for handling medical records, the bookkeeping and indexing of such records is a core concern, while logging a history of changes to the record database or user database, or an authentication system, would be cross-cutting concerns since they touch more parts of the program.
The sum of all core concerns is the business logic of a program, while all other aspects of the program are needed for proper execution, but not part of the actual business logic.
See aspect-oriented programming, separation of concerns and concern for more details.