Something that is palmary is outstanding and worthy of praise. If your school goes way beyond the target in fundraising for a charity, that's a palmary achievement.
The word palmary harks back to ancient Rome, where a palm branch was awarded to the winner of a race or other public contest. The Latin word palma gave us our word palm, and Latin palmarius, meaning "worthy of a palm branch," is the source of palmary. Palmary is usually used to describe a thing rather than a person, often an excellent specimen of a particular type: "This movie is a palmary example of film noir."