Callback Function: A function passed as an argument to another function.

A callback function in React JS is a function that is passed as an argument to another function, and is executed after the first function has finished. It allows one function to notify another function when a task has been completed. Callback functions give a way to make the flow of the code asynchronous, offering some control over the order in which functions are executed. These functions have a wide range of applications, including event handlers, timing events, and in the context of asynchronous computations where we want to pass some data from the asynchronous task to another function.

For Example,

```JavaScript
doSomething(parameter1, parameter2, function (err, result){
if (err){
console.log(err);
}
else {
console.log(result);
}
});
```

In this simple example, 'doSomething' is a function that we assume performs an asynchronous task (like fetching something from a database, accessing a web API, reading a file, etc). It takes two parameters (parameter1, parameter2), and a callback function. The callback function is executed when the task of 'doSomething' function finishes. If there's an error in the task, it sends the error object 'err' to the callback else sends the 'result' to the callback.

Thus, the flow is controlled and the result or error is handled properly with the help of the callback function.