storyboard ID

The storyboard ID is a String field that you can use to create a new ViewController based on that storyboard ViewController. An example use would be from any ViewController:

//Maybe make a button that when clicked calls this method

- (IBAction)buttonPressed:(id)sender
{
    MyCustomViewController *vc = [self.storyboard instantiateViewControllerWithIdentifier:@"MyViewController"];

   [self presentViewController:vc animated:YES completion:nil];
}

This will create a MyCustomViewController based on the storyboard ViewController you named "MyViewController" and present it above your current View Controller

And if you are in your app delegate you could use

UIStoryboard *storyboard = [UIStoryboard storyboardWithName:@"MainStoryboard"
                                                         bundle: nil];

Edit: Swift

@IBAction func buttonPressed(sender: AnyObject) {
    let vc = storyboard?.instantiateViewControllerWithIdentifier("MyViewController") as MyCustomViewController
    presentViewController(vc, animated: true, completion: nil)
}

and

let storyboard = UIStoryboard(name: "MainStoryboard", bundle: nil)