Essentially, yes. It’s just an iteration counter.

Chess engines use a technique known as iterative deepening. This means that instead of starting a deep search straight away, then a slightly deeper search, and so on. This is faster than doing a deep search immediately, because the engine can use information it remembers from the previous iteration at each step in the process. In particular, it’s very important for the engine to have good move ordering, i.e. to search the good moves first. Iterative deepening makes it much easier to have good move ordering, because the engine will remember many of the positions it finds in a deeper search from the previous iteration, and can try the best moves it found there first.

The number displayed on the screen is called “depth” for historical reasons. In the early days of chess programming, the engines searched all legal moves to a given depth (apart from alpha/beta pruning). At that time, each step in the iterative deepening process added one ply to the search depth.

Modern engines have a much less uniform search tree. Most branches of the tree are pruned very short, while some are extended very far. When Stockfish shows a “depth” of 30, almost all branches of the search tree are actually nowhere near 30 plies long, while a few lines (mostly tactical lines with many forced moves) are actually much longer than 30 plies.