。
She explained why she was late.
Literal
She [topic-は] late became reason [object-を] explained.
遅くなった理由を説明した — 遅くなった uses the ~くなる pattern ('became late'). 理由を説明する ('to explain the reason') is the standard formal construction. More neutral than 言い訳をする, which implies excuse-making; 説明する simply means explaining.