A callback URL "calls back" a web address rather than a bit of code and it can be invoked by an API method. That URL can be anything. It doesn't have to be a static URL. Often it is a script to perform certain functions. 

For eg. if you call, 

POST /api.example.com/foo?callbackURL=http://my.server.com/bar

Then, when /foo is finished, it sends a request to "http://my.server.com/bar". The contents and method of that request will vary as per Callback parameters specified in API documentations.