Johansson's stunt double has a mask that she wears during scenes to help make the switch out with Johansson less noticeable. Renner was apparently bored on set one day, and decided he wanted to try it on.
See the video below:
Renner originally posted the photo to his WhoSay account with the idea that it's what Hawkeye and Black Widow's child might look like.
Avengers: Age of Ultron opens in theaters May 1, 2015.