She appears serious in public, but is actually quite funny privately.

privately 是形容词 private 的副词形式，private 的意思是"私人的、私下的"，加上 -ly 后缀构成副词，表示"私下地、不公开地"。 privately 在这里与 in public 形成对比，强调不在公众场合时的状态。