"I understand."
It's a beautiful phrase.
It has so many uses:
1) Calming people down. (It's like a tilt switch in a pinball machine: you say the words, and the anger/tears/rage shuts right down.)
2) Communicating agreement and sympathy, even when I think the suggestion (and/or the person presenting it) are abhorrent. (And you'll note that you haven't actually agreed or sympathized.)
3) Moving a discussion along, especially when someone is determined to derail it. ("I think we all understand your concerns. Do you have any solutions in mind?" is a pleasant alternative to "Oh my god, shut up before I stick my Maglite up your keester, you pathetic, blubbering drama queen.")
4) Sapping the tension out of a situation.
5) Boosting the confidence of wayward actors, even when you have no idea what they need to hear beyond vague platitudes
6) Accepting criticism gracefully and professionally.
7) Giving criticism gracefully and professionally. ("I think I understand what was going through your mind, and I know why you made the choices you did. The difficulty is that...")
8) Shutting people up. (The jerks who love to COMPLAIN IN A REALLY LOUD VOICE about EVERY PERCEIVED SLIGHT? They never expect the words "I understand" to come out of the mouth of the person they're screaming at. Quiets them right down.)
9) For all I know, it can also avert nuclear war, create peace in Israel, and make fries julienne.
The only problem is that my assistants and superiors have heard me using it so much that they've started jokingly calling me out for you. ("You understand? Does that mean you love it or you hate it?")