According to Apple's System Status page, the iTunes Store, the iOS App Store, and the Mac App Store are currently unavailable for some users, making it impossible to do things like purchase new apps and download app updates.
The System Status page indicates the outage has been ongoing since approximately 12:30 pm. Pacific Time, which corresponds to many reports on Twitter and other social networks about the downtime.
Customers have been complaining about being unable to download apps and install app updates, with some complaints being attributed to the new iOS 10.2 update. The problem is an App Store problem rather than an issue with iOS 10.2, and should be resolved shortly.
Update: Apple's System Status page says the App Store, iTunes Store, and Mac App Store outage has ended and the services are functioning as normal.