Omakase (お任せ) is a Japanese word meaning "entrust" or "protect". It's best known in the States as a way to order sushi - you entrust the sushi chef to choose what you'll be eating, and in exchange for letting the chef set the price, you get a meal that surprises you and more often than not delights you.
When I lived in Ann Arbor many (many) years ago, I would sit at the end of the sushi bar at Miki and say "Sumimasen, Nori-san. . .omakase onegaishimasu". He would nod once and go to work, serving me at his own pace (which I suspected was the ideal pace) until he sensed I was through (regardless of whether I was full). The meal lasted just the right amount of time, with just the right number of courses for that evening and for the fish he had on hand.
You didn't have to order omakase - it wasn't advertised or even suggested. But whenever I did, I could always see someone looking at my dishes with an envious expression.
"That looks really good - what is it?" they'd ask.
"I don't know," I'd reply. "Nori-san chose it for me."
It felt like a little secret then, my omakase dinners at Miki. Over time, he became a better judge of my tastes, and I learned to trust his. I would eat at Miki even when I couldn't really afford to eat there, just to have that experience of trust given and trust rewarded again.
That was really the heart of it - I trusted Nori-san - and Nori-san worked hard to deserve my trust. In return, I was scrupulously loyal to his restaurant, and to him. I knew I'd be delighted by whatever he served. He understood me, and I think in giving him free rein to express himself through his art, he came to appreciate that I understood him as well.
The bond of trust embodied in omakase is a worthy and difficult ideal I think product managers should strive for. Put another way, I want the sort of customers who trust me to take their best interests to heart, and who will let me delight them in ways they might not even realize they wish to be delighted.