I know the new health subsidies are based on your household income, but how do they define 'household'?

“Household” only includes you, your spouse, and anyone you can legally claim as a dependent on your tax return.

 It generally wouldn’t include a non-marital relationship (such as a boyfriend or girlfriend), except under very limited circumstances.

To get more details, see page 16 of the IRS instructions for filling out Form 1040 or call the IRS (after the government shutdown ends) at 1-800-829-1040.