The postman delivers mail to each house in turn.

Literal

Postal-delivery-person [topic-は] one-house-each mail [object-を] distribute.

一軒づつ ('one house at a time, house by house') uses the counter 軒 (けん) for houses and the distributive suffix づつ/ずつ ('each, apiece, at a time'). The distributive づつ is versatile: 一人ずつ ('one person at a time'), 少しずつ ('little by little'). Note that 配る ('to distribute, hand out') is general-purpose and used for both mail and party favors.