I am a gamer and Nintendo guy, so I'll try to explain in non-gamer terms.
The Wii U is a new console, marked as such by a significantly more powerful CPU/graphics processing ability, including HD Graphics. It also had the Gamepad, a tablet like controller that enables certian functions and with many games allows you to play without needing the TV (like a portable console, only not portable). It comes with the system. The Wii U plays its own games designed for the system and does not enhance in any way games for the original Wii. It will play Wii games, and use your Wii remote controllers (for both Wii and Wii U games), but they will still be Standard Definition and be identical to the experience on Wii. You can transfer all of your saved games, downloaded titles, and Mii characters tot he Wii U with a one-time transfer.
Those are the facts, but there is more to consider. The Wii and Wii-U are both positioned as Family style consoles. They do not cater to the gamer demorgraphic that loves Call of Duty (though CoD IS available on Wii-U) and online multiplayer (it does that too, but the community is rather small). Hardware-wise, like the Wii, the system uses more modest specs, making it about equivalent to the PlayStation 3/X-Box 360 in the graphics department (PS4 and XB-ONE both coming out this month are significantly more powerful under the hood).
That all tends to be a turn-off to the gamers, but it is not necessarily a reason to not buy the platform. The Wii, despite being the weaker of the bunch, was actually very popular and was supported throughout its lifespan, mostly with family-friendly games though. You might miss out on a Resident Evil or Bioshock, but if it is primarily for your children this is not a problem. Both XBox and PlayStation attempted to emulate the family-friendly titles of Wii, and XBox at least captured some of that market with Kinect, their camera-sensor that allows controller-free play. The new Xbox One has Kinect built into the base package, so it is also something to consider.
Wii U likely will be reasonably well supported. Even though it is not selling like gangbusters as its predecessor did, history shows Nintendo has a habit of supporting consoles, and with a lot of better games on the way (Mario Kart for example) it should be a safe bet for families, and cheaper than an Xbox One or PS4. Certainly, games for the original Wii are coming to a stop, so upgrading soon is warranted. If you want the best visuals, online play, and more adult games (though plenty of kid-friendly titles are on all systems), a PS4/XB-ONE is a better bet. If you like family games, Wii Sports, Mario, and the ability to play off the TV, then Wii-U is your bet (and it still has plenty of adult and online games).
Sorry for the long post. If you have any questions, feel free to ask.