Here, great means exceptional. Great customer service means being treated courteously, with friendliness and attention to your needs in a shop, restaurant, hotel, etc.
For example, when you enter a shop, great customer service might begin with the shop assistant/owner smiling in a friendly way, saying hello, and asking if she/he could help you. If you were looking for something particular, she/he would be helpful and answer any questions you had, but not be pushy or aggressive. After you had made your purchase, great customer service might be offering to gift wrap your purchase, thanking you and wishing you a good day.
The application is asking what kind of experiences of great customer service you have received yourself and given ("delivered") to others, with examples.