Nintendo approached open-source project repository GitHub and asked it to shut down a popular Game Boy Advance emulator being hosted on the site. The emulator in question is browser-based, and does not require users to supply their own game ROM files in order to play. This means that the emulator is being bundled with illegitimate copies of Nintendo's software, constituting copyright infringement. Nintendo has chosen not to pursue immediate legal action as it did in the recent case of LoveROMS, and instead simply wants the emulator taken down. It should be noted that the code used to make the emulator run is fully visible on GitHub and is under a free and open-source license, meaning that there are bound to be forks and copies of the project for Nintendo to contend with.
For the uninitiated, an emulator program made to run console and handheld games on a computer, smartphone or other device is not illegal or infringing in and of itself. The game software and the system BIOS files of the emulated consoles are covered under copyright law, and thus must legally be supplied by users. Hosting ROMs on a website with a clearly stated rule set that dictates they only be used for backup and archival purposes, meanwhile is a legal gray area. This emulator bundles everything you need to play in a browser-based package that's not meant for end users to download, which means that the ROMs logically cannot be for archival or backup purposes, and are meant for immediate, short-form play, a clear violation of relevant laws.
This disparity of law is why big emulation sites like EmuParadise can continue to stay open, though game companies do very often file DMCA takedown notices against those sites as well. Creators of emulators are almost always within their legal rights, but bundling the games or BIOS files with the emulator can be construed as illegal even when they're for download and not immediate play. To put it as straightforward as possible, in almost all cases, if you own a game and a console, you're legally allowed to play that game in an emulator, and under no other circumstances. It should be noted that the terms of service for some games and consoles disallows even this, and in those cases, the makers of those games and consoles can go after sites and uploaders in a lawsuit, even though no criminal charges can be pursued. Nintendo is no stranger to such enforcement, and often come down hard on fan creations and derivative works as well.