Median household income is the amount that divides all households into two equal halves: half of households have income above it and half below it. A household includes all the people who occupy a housing unit, so the figure combines the incomes of everyone living together, whether or not they are related. In the United States it is measured and published every year by the Census Bureau, primarily from the Current Population Survey, and it is one of the most widely cited indicators of the economic position of a typical household.
The reason the median is used rather than the average is the point most worth understanding. An average, or mean, is found by adding up all incomes and dividing by the number of households, which lets a small number of extremely high incomes drag the figure upward and away from what most households actually experience. The median is not affected by how extreme the highest incomes are, only by where the middle falls, so it gives a truer picture of the household in the middle of the distribution. This is why economists and reporters describe the "typical" household using the median.