Households are groups within the SCA, usually based around an interest in certain areas of SCA endeavour, or friendship groups (or both!). Sometimes a peer will form a household that includes his/her apprentices/proteges/squires. Unlike other groups, such as a barony, Households aren't based on geography (although members of a household may be from a particular geographical area), they are not official groups of the Society, and any "membership requirements" of a household are at the discretion of the household. A household cannot hold official meetings or events, but they are more than welcome to run events on behalf of the official group. They may include or exclude anybody they like, whereas an official group cannot do this.
They can be a great support network, and often the activities of the household will extend beyond SCA. Another way to look at it is that a household is your "family" and the group the village/hamlet that you live in.
You do not have to be a part of any household, and just because someone is a part of a particular household does not mean that you can't hang out with them. You can even start your own household if you want to!
Examples of households in and around Stormhold include House Reverie (based around Sir Antoine le Reveur and his squires), House Woodrose (mainly an Arts and Sciences household of old broken down hacks encumbered by offspring with a few who pretend to fight once in a while when the injuries and venerability allow), Unnamed (another mostly A&S household) and the Axemen (a fighting household that is mostly demographically based around younger members with a few old, wise heads attempting to control the chaos).