For example, it used to be that only moderators could unkill a [dead] post and restore it to full visibility. Then we started an experiment in letting non-moderators do that, and this turned into the 'vouch' feature which allows most HN users above a certain karma threshold to have a say in which posts get unkilled. That was the biggest success to date - it has made a big difference both in thread quality (many interesting comments become visible) and community happiness (there's less resentment about posts being dead than there used to be).
That was a great outcome, and we're always thinking about more possibilities for such things. The current experiment is very much in the same spirit. Personally I would love to find ways to extend these things to everyone (most likely above a certain karma threshold) but it's not often obvious how to do that.
Another example is the second-chance pool (https://news.ycombinator.com/pool, explained at https://news.ycombinator.com/item?id=26998308), which gives submissions a random placement on HN's front page.