。
She sang to her heart's content.
Literal
She [topic-は] heart-goes [until-まで] sang.
心行くまで (こころゆくまで) is a literary expression meaning 'to one's heart's content, until fully satisfied.' The 行く is the classical form of 行く meaning 'to go (to a state of satisfaction),' and まで marks the endpoint. It's an elevated, somewhat poetic expression — everyday speech might use 思いっきり ('to the fullest') or 好きなだけ ('as much as one wants') instead.