Like the Xbox 360, your pins on Xbox One are saved to the cloud, meaning you can access them from anywhere as long as you're online. However, also like the Xbox 360, they are not stored locally for offline access.  

This makes sense for some applications; you can't use Netflix or ESPN without an Internet connection. However, you can also pin games in that area – including offline games – in order to avoid sifting through menus. Without being connected online, you don't get that convenience on Xbox One because of the way the console stores its data.

When your Xbox One is online, you see your array of pins (above). If your console is offline, you see this instead:

Of course, the Xbox 360 doesn't let you use pins if you're offline, either – a restriction that some users were hoping Microsoft would rectify with the new console. Oh, well. Maybe a future update will allow users to store that information locally as well as to the cloud.