This means that, so long as the owner of the Xbox One is a Gold subscriber, other people in the household will be able to have their own accounts and Gamertags, without having to sacrifice access to Gold-level services such as online multiplayer, DVR functionality and so forth. Gold privileges will also follow subscribers to other people's Xbox Ones, so if you have a Gold account and visit a friend who doesn't, you'll both be able to use Gold features for as long as you're logged in on their console.
Microsoft also announced that similar functionality will be applied to digital versions of Xbox One games. When someone purchases and downloads a game onto their console, every one of that console's users will also have access to that game, regardless of whether the person who purchased it is signed in (Xbox 360 games work similarly now). Similarly, every game you've purchased digitally will be available to you on any Xbox One that you sign in on.