Best, worst and average case

The same algorithm can do very different amounts of work on two inputs of the same size. The worst case is the most work it does on any input. The best case is the least, and the average case is what you expect on typical or random input.

Linear search, which checks items one by one, finds its target on the first step at best and checks everything at worst. Quicksort averages O(n log n) but slows to O(n²) when it keeps choosing bad split points (pivots). When someone gives one Big-O without saying which case, they almost always mean the worst. That is the case that decides whether your code finishes on the input you did not expect.