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She got excited at the thought of meeting the famous singer.
Literal
She [topic-は] that famous singer [to-に] can-meet [quotative-と] think [when-と] became-excited.
わくわくする is a 擬態語 (state mimetic) for the buzzing, fluttering excitement of pleasant anticipation — the kid-on-Christmas-morning feeling. The construction ~と思うと is doing double duty here: と思う marks 'thinking that...,' and the second と is the conditional/temporal 'when/whenever,' so the whole phrase reads 'whenever she thought about meeting...' — the excitement re-triggers each time the thought returns. 会える is the potential form of 会う ('can meet'), which takes に for the person met (友達に会う, not 友達を会う).