Pretendo is a recreation of the Nintendo Network, Nintendo’s online networking infrastructure for 3DS and Wii U software. It’s still under development, but when it’s fully operational it may even be able to resurrect lost and lamented services like Miiverse and Wii U Chat.
To help avoid legal entanglements it’s a clean-room reimplementation that doesn’t use Nintendo confidential documentation, which does slow their work, and users will have to make new accounts since they don’t have access to Nintendo’s account information (and wouldn’t want it if they did have access).
Even when Pretendo is usable by normal users, unless you’re playing using an emulator (Cemu is the only one that supports it), you’ll have to hack your system to use Pretendo’s servers. Currently the servers for some 3DS and Wii U games are still operational, but it’s only a matter of time before Nintendo shuts them down, just like they did with the Wii, despite its popularity. It is nice to know that people are working for replacement infrastructure for that eventuality.
A similar service, Wiimmfi, is in operation to replace the Nintendo Wi-Fi Connection that Wii and DS games used.