This is the 15516th most frequent Russian word.
премией
"Премией" means "prize" or "award" (instrumental case).
In this sentence, "премией" is used as an instrumental case noun, indicating the means by which he was honored.
Он был удостоен премией за его выдающиеся достижения.
He was awarded a prize for his outstanding achievements.
Here, "премией" is instrumental again, showing what the competition was aiming to achieve.
Школьники соревновались за премией за лучшее сочинение.
The schoolchildren competed for a prize for the best essay.
"Премией" is instrumental case here as well, emphasizing the grant as a source of assistance for the project.