When I'm observing a game, the evaluation bar works and above the moves list, there is a numerical value for depth. But what is Stockfish depth and what does it measure or tell?
2 Answers
See the Chess Programmming wiki on depth. It is nominally a measure of how far ahead an engine is searching, so e.g. an engine that is looking at depth = 10 is looking five moves ahead (10 ply = 5 moves). "Nominally" because these days there are all sorts of pruning techniques and quiescent searches and similar that makes the number itself relatively meaningless; however, in terms of playing strength, a higher number is still always better than a lower one. As you let Stockfish run, you should see that its depth continuously increases, as well.
Depth means roughly nothing. It used to mean the depth in the search tree that an engine searched but with modern search algorithms, there is enough pruning that the depth becomes fairly non-informative.
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This answer would benefit from more details or with some citations to be more valuable for future visitors. For example, "with modern search algorithms, there is enough pruning that the depth becomes fairly non-informative" [citation needed] Jan 11 at 15:18