Neo4j 3.0 introduces a new feature called user-defined procedures, which allow developers to extend the Cypher query language with custom functionality. These procedures can be used to add new capabilities and improve performance in graph algorithms. The APOC procedure library provides a collection of pre-built procedures that cover various areas such as graph algorithms, metadata, and data integration. With APOC, developers can easily create custom procedures using Java or other JVM-based languages, making it easier to integrate Neo4j with other databases and tools. The library also includes features like metadata capabilities, date and time functions, and export procedures for exporting database data in Cypher format.