If a sorting algorithm is said to be "unstable", this means that for any items that rank the same, the order of the tied members is not guaranteed to stay the same with successive sorts of that collection. For a 'stable' sort, the tied entries will always end up in the same order when sorted.
For an example of applications, the quick sort algorithm is not stable. This would work fine for something like sorting actions by priority (if two actions are of equal priority, you would not be likely to care about which elements of a tie are executed first).
A stable sorting algorithm, on the other hand, is good for things like a leaderboard for an online game. If you were to use an unstable sort, sorting by points (for instance), then a user viewing the sorted results on a webpage could experience different results on page refreshes and operations like paging through results would not function correctly.
