This tends to happen when you leave the game in a mid-turn state as suggested by JohnoBoy. I have even had it skip me guessing their word and going right on to select (Since I have a few high streaks though this was disconcerting to me).
I found that, on the iPad, finding the constantly running application and shutting it down, then starting the app back up again fixed the issue, let me see the person guess my word again and then me guess there's and Then pick a new word... which really sucked.
But anywho, removing the app from memory generally will reset the position of the turn between you and the other person.