Subscribe boxes are fairly standard. I could have easily mocked up a couple of fields with a "subscribe to our newsletter" heading and a submit button. But I wanted to do something a bit different. I thought it would be cute to have the popover window in the shape of a letter, with the user filling out their address details on the front. Clicking "send" then sends off the letter, which the user will receive in a few minutes as a "confirm your subscription" email.
I was initially worried about the strange placement of the "send" button, since it's not particularly intuitively placed for a user. I think a lot of users are used to hitting enter to submit a form anyway. But I don't know, moving it to the bottom right might still be beneficial for usability.