What are the "First Responder" and "Exit" boxes purpose in the storyboard editor?

I've never used it and probably never will but you can assign an object to be the first in line to receive the events from the UI.

I suppose you could be creating a UIView subclass and add it in to a UIViewController but you actually want some other object to receive and process the events other than the UIViewController you are adding it to.

I found this link which kind of explains it a bit better.

There are no good answer for this question, so I am posting my answer:

From here:

Note: You probably won’t be using the First Responder very much. This is a proxy object that refers to whatever object has first responder status at any given time. It was also present in your nibs and you probably never had a need to use it then either. As an example, you can hook up the Touch Up Inside event from a button to First Responder’s cut: selector. If at some point a text field has input focus then you can press that button to make the text field, which is now the first responder, cut its text to the pasteboard.

Edit:

1) First Responder is very useful if you are using text fields with keyboard notifications. I use it to make keyboard disappear, make an outlet to variable currentFirstResponder of your class, and in viewWillDisappear:

[self.currentFirstResponder resignFirstResponder];

2) You can read about unwind segues ("Exit" box) here