Probably not the dictionary definition, but a callback usually refers to a function, which is external to a particular object, being stored and then called upon a specific event.
An example might be when a UI button is created, it stores a reference to a function which performs an action. The action is handled by a different part of the code but when the button is pressed, the callback is called and this invokes the action to perform.
C#, rather than use the term 'callback' uses 'events' and 'delegates' and you can find out more about delegates here.