Similar in functionality to guilds in your more traditional MMORPG, the family is a collection of players who play together to increase family status. Family status is reflected in each individual player's scores so preserving and helping the family become a critical part of game play. Nothing can prevent a family from having a Lydia among them, but the more fortunate families may also have a Fanny or an Emma. The family must pull together in crises lest everyone in the family be hindered from the best virtual life has to offer.
As of April 2015, Release 17.3, we have a very basic family system in place. You can adopt, hire, propose to or marry someone, or undo all of these things, by clicking on the person, and then on the button with the family on it (currently bottom left of the row of buttons on the right), which will bring up a table of options.