The household is "the basic residential unit in which economic production, consumption, inheritance, child rearing, and shelter are organized and carried out"; [the household] "may or may not be synonymous with family". 
In economics, a household is a person or a group of people living in the same residence.
Most economic models do not address whether the members of a household are a family in the traditional sense. Government and policy discussions often treat the terms household and family as synonymous, especially in western societies where the nuclear family has become the most common family structure. In reality, there is not always a one-to-one relationship between households and families.
For statistical purposes in the United Kingdom, a household is defined as "one person or a group of people who have the accommodation as their only or main residence and for a group, either share at least one meal a day or share the living accommodation, that is, a living room or sitting room" National Statistics.
The United States Census definition similarly turns on "separate living quarters", i.e. "those in which the occupants live and eat separately from any other persons in the building" . A householder in the U.S. census is the "person (or one of the people) in whose name the housing unit is owned or rented (maintained);" if no person qualifies, any adult resident of a housing unit is a householder. The U.S. government formerly used the term head of the household and head of the family to describe householders; beginning in 1980, these terms were officially dropped from the census and replaced with householder. 
The official definition from http://quickfacts.census.gov/qfd/meta/long_71061.htm is clearer:
"A household includes all the persons who occupy a housing unit. A housing unit is a house, an apartment, a mobile home, a group of rooms, or a single room that is occupied (or if vacant, is intended for occupancy) as separate living quarters. Separate living quarters are those in which the occupants live and eat separately from any other persons in the building and which have direct access from the outside of the building or through a common hall. The occupants may be a single family, one person living alone, two or more families living together, or any other group of related or unrelated persons who share living arrangements. (People not living in households are classified as living in group quarters.)"
Most economic theories assume there is only one income stream to a household; this a useful simplification for modeling, but does not necessarily reflect reality. Many households now include multiple income-earning members.
In Social Work the household is a residential grouping defined similarly to the above in which housework is divided and performed by householders. Care may be delivered by one householder to another, depending upon their respective needs, abilities, and perhaps disabilities. Different household compositions may lead to differential life & health expectations & outcomes for household members. Eligibility for certain community services and welfare benefits may depend upon household composition.
In Sociology 'household work strategy', a term coined by Ray Pahl,  is the division of labour between members of a household, whether implicit or the result of explicit decision–making, with the alternatives weighed up in a simplified type of cost-benefit analysis. It is a plan for the relative deployment of household members' time between the three domains of employment: i) in the market economy, including home-based self-employment second jobs, in order to obtain money to buy goods and services in the market; ii) domestic production work, such as cultivating a vegetable patch or raising chickens, purely to supply food to the household; and iii) domestic consumption work to provide goods and services directly within the household, such as cooking meals, child–care, household repairs, or the manufacture of clothes and gifts. Household work strategies may vary over the life-cycle, as household members age, or with the economic environment; they may be imposed by one person or be decided collectively.
Feminism examines the ways that gender roles affect the division of labour within households. Sociologist Arlie Russell Hochschild in The Second Shift and The Time Bind presents evidence that in two-career couples, men and women, on average, spend about equal amounts of time working, but women still spend more time on housework. Feminist writer Cathy Young responds to Hochschild's assertions by arguing that in some cases, women may prevent the equal participation of men in housework and parenting.
Household models in anglophone culture include the family and varieties of blended families, share housing, and group homes for people with support needs. Other models of living situations which may meet definitions of a household include boarding houses, a house in multiple occupation (UK), and a single room occupancy (US).
In feudal or aristocratic societies, a household may include servants or retainers, whether or not they are explicitly so named. Their roles may blur the line between a family member and an employee. In such cases, they ultimately derive their income from the household's principal income.