Nintendo, just like all games companies, wants you to buy gaming hardware and then buy lots of games for it. Anyone deciding to modify or hack hardware in order to play pirate games, run emulators, or use a system for homebrew development does so at their own risk, and right now, that risk is a ban for 3DS owners.
Reports are appearing across multiple forums including GBATemp and Reddit, that Nintendo is clamping down on modified 3DS hardware and blocking access to online services. Those affected are seeing "Error Code: 002-0102" appear at the top of the lower 3DS screen along with a message stating online services are restricted. It doesn't matter what model of 3DS you own, the ban applies to any and all models Nintendo detects as having been modified.
Kotaku got in touch with Nintendo and was told the bans are in response to, "unauthorised system modifications, playing unauthorised versions of one or more games and/or connecting to the game servers in violation of our terms of service." The ban apparently blocks access to playing games online and accessing services such as Miiverse. However, the eShop is still accessible, but apps such as YouTube are blocked. A banned 3DS can still be used to play games offline, but a new 3DS will be required to play online again.
According to a post on GBATemp by user PF2M, Nintendo collects information every time you connect to its online services to play games, run apps, etc. This information collection is ongoing and hasn't really been used for much until now. But PF2M believes Nintendo decided it was time to start using the data, and that "Nintendo knows all." So if you have a modified 3DS and don't want to get banned, either remove the modification or don't access Nintendo's servers.