User-defined functions (UDFs) are functions created by users to extend the functionality of a programming language or database system. In the context of databases, UDFs allow users to define custom logic or calculations that can be reused within the database. They offer advantages such as reusability, abstraction, performance optimization, customized logic, and modularity. UDFs enhance the capabilities of a database system by providing users with the flexibility to define and execute their own functions tailored to their specific needs.