Lots of operations within libcurl are controlled with the use of callbacks. A callback is a function pointer provided to libcurl that libcurl then calls at some point in time to get a particular job done.
Each callback has its specific documented purpose and it requires that you write it with the exact function prototype to accept the correct arguments and return the documented return code and return value so that libcurl will perform the way you want it to.
Each callback option also has a companion option that sets the associated "user pointer". This user pointer is a pointer that libcurl doesn't touch or care about, but just passes on as an argument to the callback. This allows you to, for example, pass in pointers to local data all the way through to your callback function.