Definition:
The cross-cutting concern is a concern which is applicable throughout the application and it affects the entire application. For example, logging, security and data transfer is applicable for every module of an application hence they are cross-cutting concerns.
For instance, if writing an application for handling medical records, the 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 interact with more parts of the program.
Further Reading:
Book: Applying UML and Patterns by Craig Larman