In asking this question, your potential employer is looking to see that you are prepared to go above and beyond the call of duty when the company needs you.
But you have to be careful when answering, as it is easy to fall into the trap of slagging off your current employer or seeming disorganised. Your interviewer does not want to hear how your current boss failed to provide you with resources or that you once pulled an all-nighter to meet a university deadline.
An ideal answer will centre round the busiest time of your company’s year (i.e. the Christmas rush in retail). In your example you should outline the reason for your stretched deadline and say what you did to ensure that you met it.