What does 4000 VA mean?

Technically, VA is the RMS voltage times the RMS amps. When the voltage and current are the same waveform and are perfectly in phase, the power factor is 1, and VA = watts. When the voltage and current waveforms aren't identical and in phase, the resistive losses in the generating and transmission apparatus are higher. Some of the power that would ideally go to the load instead goes up as heat. The inverter and generator manufacturers want you to think that their equipment is rated in watts, but when you get to the real specs, the power is rated in VA. The consuming device manufacturers want you to know how many watts the device consumes, and want to keep quiet about the VA. Power factor correction in motors is fairly easy with passive components. In a switching power supply, active circuitry is required for correction, which is probably why it's not more widespread as of yet. Don't know if it will help or not, here are a few reads that might help connect a dot or two before they go off into the highly technical weeds:

http://www.aptsources.com/resources/pdf/PFC.pdf
http://www.aptsources.com/resources/pdf/Power%20Factor%20V%20Crest%20Factor.pdf
http://www.aptsources.com/resources/pdf/True%20vs.%20Apparent%20Power.pdf