An anytime algorithm monotonically improves some evaluation metric. For a sort, the evaluation metric is usually the number of inversions in the list. At completion, there will be zero inversions. If at time 0 there are N inversions, then at time 0 < t < completion time there will be ≤ N inversions; that is, the list is "more sorted" than it was before. As the various examples about games and animation elsewhere in the comments show, this can be interpreted as "somewhat smoothly moving towards sorted over time," which is an (occasionally) ((rarely)) useful property.

Okay, but it gives you a mostly good answer! Unlike many other sorts where if you interrupt it before the last step, you get total nonsense.

It's basically asymptotically approacting the correct (sorted) list instead of shuffling the list in weird ways until it's all magically correct in the end.

> Unlike many other sorts where if you interrupt it before the last step, you get total nonsense.

which ones you have in mind? and doesn't "nonsense" depend on scoring criteria?

selection sort would give you sorted beginning, cocktail shaker would have sorted both ends

quick sort would give vast ranges separation ("small values on one side, big on the other"), and block-merge algorithms create sorted subarrays

in my view those qualities are much more useful for partial state than "number of pairs of elements out of order" metric which smells of CS-complexity talk