She was eagerly waiting for her husband to come home.
Literal
She [topic-は] husband's return-home [object-を] yearned-for.
待ち焦がれる is a compound verb: 待つ ('to wait') + 焦がれる ('to yearn/pine'). Together they express eager, anxious waiting. 帰宅 ('returning home') is a formal Sino-Japanese compound.