Callbacks are the execution of script functions or methods by C++. HeroEngine runs scripts at specific HSL Entry points. These entry points are into well-defined scripts with well-defined function signatures. The specific function or method being called by C++ in the entry point script, will then call other functions as-needed to process a particular event.
A typical callback is via the Chat System:
When the Server receives a chat message from the client, C++ will then call _GotChat method on the $CHAT System Node. The $CHAT script will then call an overridable method to process the event in a game-specific fashion.