We doing this now? Alright, here we go:
NX refers to a software platform build by Nintendo with new partners, emphasizing ease of development and system-wide connectivity. When it is announced, a new handheld is shown using it, but Nintendo makes a point of stating that all future Nintendo consoles will also use NX. The purpose is to make it more attractive to outside developers, as their titles have a wider market and greater longevity, but it also eases pressures on Nintendo's internal studios who sometimes have to redo unannounced work several times because of console cycle changes.
The handheld is a compromise on the Wii U gamble. It features the same functionality as the Wii U game pad, slimmed down and given a capacitive touch screen, but works as a stand-alone console. Packed with it is a wireless HDMI dongle that acts as a video and audio receiver from a connected NX device. Only one device can connect to it, but multiple NX devices can connect and stream video between each other, so as long as the "host" device is powered on, players can bring their own and play split-screen on the television.
For players who would like backwards compatibility, a device is sold separately which accepts Wii and Wii U discs, and has HDMI ports to accept the handheld's wireless dongle and a cable to connect to the television. The device uploads game data to the handheld, and players can choose which screen to play the game on as they can with the Wii U now.
The system launches with what Nintendo thinks is a strong lineup, but fans are only really interested in the handheld ports of the Metroid Prime trilogy and Splatoon. Because the platform is meant to be long-lived and attractive to third parties, Nintendo is content to release only a new Fire Emblem game in the first year, padding the rest with ports of their popular games from previous systems. Square Enix treats the system poorly, opting to churn out two or three cheap spin-offs instead of a decent original title, and Atlus has to fill in for them again. Capcom tests the waters with a port of their newest iteration of Street Fighter before trying a new IP. It lacks mass appeal, but develops a strong enough cult following to justify a misguided sequel before fading into obscurity.