A Household represents a person, group or family's home or location. It contains information that is shared by everyone in it, and every Person record belongs to a Household. So in order to delete a Household it can no longer contain any people.
The first steps for deleting a Household then, will be to clear it of people by deleting them, moving them to other Households or, if a person was accidentally created twice perhaps, by combining the duplicate information under a record in another household. See articles for each of these tasks below:
Move-a-Person-to-a-Different-Household
Combine-Duplicate-Person-Information
Deleting the people does not automatically delete the Household, but once a Household no longer contains any people, it is very easy to delete. Just go to the Households grid, highlight the Household in question and click Delete at the bottom of the grid.