Seriously; in earnest. Used to indicate doing something with genuine effort or to express surprise/doubt (e.g. 'Really?').
本気で留学を考えているなら、まず語学の勉強を始めなさい。
If you're seriously thinking about studying abroad, start studying the language first.
彼女は本気で怒っているようだった。
She seemed genuinely angry.
本気で言ってるの？冗談でしょ？
Are you serious? You're joking, right?
試合に向けて本気で練習を始めた。
He started practicing in earnest for the match.