A house is where the residents of your town live. The house provides the occupants with warmth and shelter, a place to raise a family, and a place to store goods that they use.
A family will stock their home with food and fuel to keep themselves well fed and warm. As the family grows, children that reach adult age will start looking for their own home and a spouse. Unless empty homes are available, they will continue to live with their parents, and produce no children of their own - each house can hold up to 8 people.
Later on in the game, you will want to upgrade to stone houses, as these use less firewood to keep warm.
Heating
Wooden homes are easy to build but use more fuel to heat than stone houses. Wooden houses each burn an average of 30 firewood or coal each year (this amount depends on the length of the winter).
Styles
There are 6 different types of wooden house - press f when placing the house to cycle between the styles.