First of all, the spelling is correct above. Not to be so nitpicky, but I have to cringe when many of you are misspelling (and probably mispronouncing) the term. To me, it's like calling a pizza a "pazza". Okay, now that I got that out of the way, allow me to set a chow definition. An omakase meal at a japanese restaurant (doesn't necessarily have to be sushi, BTW) is an interactive process between you (the diner) and the chef. The chef will normally ask if you have any dietery restrictions, and he/she will provide you with many small dishes or pieces of sushi until you indicate that you've had enough, or if the chef has hit a dollar ceiling that you may have negotiated before the meal. In other words, it's an interactive dining experience.
Here are some things Omakase is NOT in my definition. Although it may say it on a menu, omakase is not an assortment of sushi (as in a regular or deluxe sushi set) chosen by the chef. Okay, the chef chooses what pieces to serve, but I wouldn't call this an omakase dining experience. Omakase is not a set multi-course dinner option (without sustitutions). That is more likely to be what is called kaiseki. For an example, at a very good sushi place in NYC called Jewel Bako, you can choose a number of set menus at three different pricing levels. They call this omakase, but it's not. These dining options resembles kaiseki style dining or french degustacion (or tasting) menu. Again there lacks an interactive component that makes an essential omakase experience.
Okay, got that off my chest. Thanks for listening.