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.
彼は勤め向きが合わなくて、すぐに辞めてしまった。
The nature of the job didn't suit him, so he quit right away.
勤め向きは主に経理です。
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'.