We played quite a few games and we had prizes for the winner of each of the games.

quite 是副词，表示"相当、很"，用于加强语气。 a 是不定冠词，表示"一个"。 few 是形容词，表示"很少的、不多的"。 quite a few 是一个固定短语，字面意思是"相当少"，但实际表示"相当多、不少"，带有反语的意味。