Used adverbially to mean doing something as much as one wants, not limited to eating. Often with verbs like 遊ぶ, 泣く, 話す.
On my day off, I played to my heart's content.
She cried her heart out.
Standard kanji-kana spelling.
Alternate spelling using the kanji 一杯.
Compound of お腹 (stomach, with honorific prefix) and 一杯 (full). The extended adverbial sense 'to one's heart's content' developed from the idea of filling the stomach to satisfaction.