elder sister's husband; brother-in-law
Refers specifically to the husband of one's older sister. Not used for a spouse's brother or a younger sister's husband.
My elder sister's husband is a doctor.
姉婿と一緒に釣りに行った。
I went fishing with my brother-in-law (my elder sister's husband).
Compound of 姉 (ane, 'elder sister') and 婿 (muko, 'husband, son-in-law'). The reading あねむこ is a straightforward combination of the kun'yomi readings of the two kanji.