This option won't show up if your Sim doesn't have kids or isn't living in a house with their kids.
Anyways, your Sim can now ask their friends to watch the kids at their houses just like the Sims can ask their neighbors/friends to watch the kids at their apartment lots.
This lets Sims have more options to have someone other than a nanny watch their children. The friend will act like a nanny and take care of the kids while the parents go to work or go out or do housework without interruption.
Plus babysitting is free! Friends don't charge for that.
Must have at least 50/0 to 70/0 with the Sim you want to ask to watch the kids. This option also won't show up if your Sim isn't friends with the Sim you want to babysit.