She answered with a radiant smile.
卒業式は晴れやかな雰囲気に包まれていた。
The graduation ceremony was filled with a bright and cheerful atmosphere.
晴れる is a verb meaning 'to clear up' (weather) or 'to be dispelled' (doubts, gloom). 晴れやか is an adjectival noun describing the resulting bright, cheerful state.
明るい is a general i-adjective for 'bright' or 'cheerful'. 晴れやか emphasizes a clear, unclouded radiance, often with a more elegant or literary nuance.
Derived from the verb 晴れる (to clear up) with the adjectival suffix やか, which often forms na-adjectives describing a state or quality.