For example, recently I showed up to a yoga class, and there was construction going on the street outside, so that it was mildly inconvenient to get to the parking lot. The yoga instructor apologized profusely for the inconvenience.
I didn't understand why I'd want to be apologized to for this: not only was it outside her control, but the inconvenience was trivial. I felt slightly less at ease after such an apology.
But looking around at others, it was quite obvious that this gesture had had the intended effect. I guess, in this regard, I am the odd one out.