* Captains awards: This is plural and implies there are multiple awards given out by the captain(s).
* Captain's award: This is singular and implies there is a single award given out by the captain.
Here are some examples:
Plural: "The team was excited to receive the captains awards for their hard work."
Singular: "The captain presented the captain's award to the player with the most assists."
Without more context, it's impossible to tell which is correct.