I wish I had heard of this term before; the concept is quite familiar.
Mono no aware (物の哀れ), literally "the pathos of things", and also translated as "an empathy toward things", or "a sensitivity to ephemera", is a Japanese term used to describe the awareness of impermanence (無常 mujō), or transience of things, and a gentle sadness (or wistfulness) at their passing.
Search prompted by a Roger Ebert review of “Moonrise Kingdom” starring (among others) Bill Murray:
Murray is always right for a role in an [Wes] Anderson film, and I wonder if it’s because they share a bemused sadness. You can’t easily imagine Murray playing a manic or a cut-up; his eyes, which have always been old eyes, look upon the world and waver between concern and disappointment. In Anderson’s films, there is a sort of resignation to the underlying melancholy of the world; he is the only American director I can think of whose work reflects the Japanese concept mono no aware, which describes a wistfulness about the transience of things.