Shy Penis is a term used to describe a general state of shock exhibited by one's penis in the presence of other men, most particularly when attempting to urinate.
Ted stands by the urinal and pops it out just as Ralph walks into the bathroom. Ted waits and waits and waits, but is unable to force the pee out.
Ralph: What's taking so long? I have to go!
Ted: Seem to have a slight case of shy penis.