They work by automatically feeding wood pellets into the stove's firebox. They have the advantage of not using fossil fuels, and not contributing to the buildup of greenhouse gases in the atmosphere. They are very clean burning and if they have a window you can sit and watch the glow of the firebox. On the down side, having mechanical feed systems and forced air blowers, they are dependent on electricity to function, and they are noisy. They require the purchase of a manufactured fuel, which may not be available where you live.
Pellets are more expensive than firewood.
And, last but not least, watching the glow as the pellets are fed into the firebox can't compare with watching the fire in one of our woodstoves. We have the same reservations about corn stoves, which are economic but rely on electricity, expensive fuel, and lack ambiance. Gas stoves are another attempt to provide the woodstove experience with greater convenience. And, if you live in a big city where you just can't get wood, they may be a satisfactory substitute. But, they aren't woodstoves.