MelyndaModified Sine wave makes a very square wave, it's sort of like a box, as a result it causes a pulse. The power goes from 120 to 0 and back. Cheaper and very sensitive devices can have problems, as there is time between each pulse where there is no power. It sounds far worse than it is, because we run our power at 60hz, so it pulses 60 times a second. They can be quite noisy if not well designed, and so you don't want to run noise sensitive equipment on them, such as an audio amplifier.
A pure sine wave looks like a sweeping curve, as the power sweeps from 120 to 0, like a fade out. As a result it's much easier on device inputs, especially if they are built super cheap and don't have enough capacitance. That's because the power is never really off, as the sweeping wave passes through 0V on the way to peaking at 120v.
Pure sine wave AC power production from a DC source, requires a lot more hardware and costs significantly more as a result than a modified sine wave source.