chai.spy.callsBackWith simply creates a spy that expects the last argument it was called with to be a callback function and calls it with the arguments provided in its constructor.
var methodA = chai.spy.callsBackWith(new Error('foo'));
methodA(cb);
// cb would be called with one argument: new Error('foo')
var methodB = chai.spy.callsBackWith(null, {id:12});
methodB(cb);
// cb would be called with two arguments: null and {id:12}
chai.spy.callsBackWithsimply creates a spy that expects the last argument it was called with to be a callback function and calls it with the arguments provided in its constructor.