one's song repertoire; songs one can sing
Refers to the set of songs a person knows and can perform, especially at karaoke or social gatherings.
His repertoire consists mostly of enka songs.
カラオケで持ち歌を披露した。
I performed my signature song at karaoke.
Compound of 持ち (mochi, 'holding' or 'possessing') and 歌 (uta, 'song'). The exact historical derivation is uncertain, but the word naturally describes songs one 'holds' in one's repertoire.