Some DC to AC power inverters produce "cleaner" power than others, leaving power inverters in the market not all being created equal. Simply stated AC power has a perfectly smooth and clean "sine wave" clean; anything else is dirty. A sine wave has a naturally smooth geometry, like the track of a swinging pendulum. It is the ideal form of AC power, running motors, and electronics designed for it, most efficiently. The utility grid produces sine wave power in its generators, and (normally) delivers via transformers and transmission lines to the customer. The AC power from the "grid" is relatively free of distortion, but there is some. A PURE SINE WAVE inverter can deliver cleaner, more stable power than most grid connections, and is how computer server rooms, hospitals, records rooms, and banks operate because of the stability.
Then there are, the rest of the inverters on the market. A "modified sine wave" inverter is less expensive, as it produces a distorted square waveform that resembles the track of a pendulum being slammed back and forth by hammers. In truth, it isn't a sine wave at all, and is represented by the red line in the graphic above. The misleading term "modified sine wave" was invented by advertising people to make you think they are "Close Enough". Engineers prefer to call it "modified square wave," for accuracy purposes.
A modified square wave, or modified sine wave inverter, produces power that you can audibly hear in flourescent fixtures, will make motors run "Hot" leading to premature failure, and can blow up some electronics that use the timing of the wave for internal systems. The corners of the 'Modified Sine Wave' can do serious damage to any sensitive piece of equipment. Long story short, a modified wave inverter makes whatever you are running work harder, except for heaters.
Conclusion: If you are buying a power inverter for simple, portable, and temporary power, a modified sine wave inverter is a reasonably disposable piece of equipment to allow you to do it. However for long term installations, and for serious equipment, a professional grade "pure sine wave" AC inverter should be selected for the job.