master of the household; head of the family
A somewhat formal or literary term for the person who leads a household, often implying authority and responsibility. Not used for modern casual 'head of the family' in everyday conversation.
As the master of the household, he has supported his family.
家長 is a more common and neutral word for 'head of the family', whereas 一家の主 carries a slightly more formal or old-fashioned nuance.
Compound of 一家 (one family/household) + の (possessive particle) + 主 (master/head). The reading あるじ for 主 is an older native Japanese word for 'master' or 'owner'.