Fig.: to be an unwelcome third party, especially being around a couple out on a date

 It has been a deadly and embarrassing evening. They invited me out of courtesy, but there was obviously something going on between them, and I felt like a third wheel

È stata una serata noiosissima e imbarazzante. Mi hanno invitato per pura cortesia ma era chiaro che quei due se l'intendevano e a me è toccato fare da terzo incomodo

John and Linda are very nice to me ever since my boy-friend left me. They keep inviting me to go out with them, but I'd rather not go because I would feel like a third wheel

Gianni e Linda sono molto gentili con me da quando il mio ragazzo mi ha lasciato e mi invitano sempre a uscire con loro, ma preferisco non andare perché non mi piace reggere il moccolo

The expression alludes to the fact that a third wheel would be of no use, therefore unnecessary, on a two-wheeled vehicle