Alternating current (AC) has a continuously varying voltage that swings from positive to negative. This has great advantages in power transmission over long distances. Power from your power company is carefully regulated to be a perfect sine wave, because that is what naturally comes out of a generator, and also because sine waves radiate the least amount of radio power during long distance transmission.
On the other hand, a sine wave is expensive to make in an inverter, and many sine wave techniques use heavy, inefficient transformers. The most inexpensive way to make AC is to switch the DC on and off–a square wave. A modified sine wave is scientifically designed to simulate a sine wave in the most important respects so that it will work for most appliances. It consists of a flat plateau of positive voltage, dropping abruptly to zero for a while, then dropping again to a flat plateau of negative voltage, back to zero for a while, then returning to the positive voltage. This pause at zero volts puts more power into the 60HZ fundamental than a simple square wave does, so it is called “modified sine wave” instead of “square wave.” Because the MOSFETs only have to turn completely on and completely off the dissipate he least amount of heat for the power generated, and so smaller semiconductors and heat sinks are needed than if you were trying to generate a real sine wave.