one's business; one's duties
Refers to the nature or scope of one's work, often used in contexts like discussing job suitability or describing what one does for a living.
The nature of the job didn't suit him, so he quit right away.
My duties are mainly accounting.
Standard kanji spelling.
Kana spelling for the first part is sometimes seen, but the full kanji form is more common.
Compound of 勤め (tsutome, 'work, service') and 向き (muki, 'direction, suitability'). The exact historical derivation is uncertain, but the combination naturally yields the meaning 'the direction/nature of one's work'.