funeral home; undertaker's office
Refers to the business or company that provides funeral services, not the physical funeral hall itself (which is often 葬儀場 or 斎場).
I contacted the funeral home and asked them to arrange the funeral.
Compound of 葬儀 (funeral) + 社 (company, shrine). The exact historical derivation is uncertain, but the word follows a common pattern for naming service companies.