Fast in the Demo, Slow for Users: Best, Worst and Average

Explain why a search that was instant in your demo is slow for users, name its best, worst and average cases, and see why Big-O usually promises the worst one.

Updated

Cheat sheet: Fast in the Demo, Slow for Users: Best, Worst and Average
Category
Data Structures
Level
Apprentice
Tags
Average Case, Best Case, software-development, Worst Case