A fatbike is an off-road bike with large, over-sized tyres - generally around 4-inches in width compared to a mountain bike which use a 2-inch tyre.
The fat bike was developed for use on soft unstable terrain, like snow and sand.
With large tyres you can also easily roll over large bumps making for a smoother ride.
They also look fantastic!
The downside to a fat tyre bike is the increased rolling resistance making them hard work to ride compared with a traditional bicycle. That's is were an electric fat bike really shines as the motor takes up the slack for you.