、。
Smiling brightly, she waved at me.
Literal
Brightly smile [while-ながら], she [topic-は] me [dative-に] hand [object-を] waved.
~ながら = 'while doing X.' Attaches to the verb stem and marks simultaneous action — Japanese's compact way to express 'doing Y while doing X.' 手を振る ('wave one's hand' = 'to wave') is the set collocation. 明るく is the adverbial form of 明るい ('bright, cheerful').