Can anyone explain how this works? What are the advantages or disadvantages?

I am thinking it has to do with gear ratio and matching engine revolutions; in other words, if in second gear, the engine spins up to 7500 rpm, when shifted to third, it drops to 5500 rpm, then when shifted to fourth from 7500 rpm it again drops 5500 rpm, and so on.

I don't realy know what you're on about, but from the description it seems like the sort of gearing you would use to keep the engine in the peak power/torque range after shifting.

Could you clarify the question? If you always change up at the same rpm value, and after the shift, the rpms drop to the same value each time, then you have equally spaced your gearing, which is not usually ideal.

why? as far as i understood the shifting problem as itself, you have to keep the engine revs in the optimal corridor of power and torque.
thus the corridor doesn't shift while moving faster, you still have to keep the gears within the corridor to get the maximal power/torque...
Or not?

Sorry for the lack of information on my part; I am ignorant with the terminology but I have heard the phrase used, but do not understand why "cross gearing" is advantageous.

A link:
http://www.spoonsports.us/catalog/products/crossGear.htm

I think cross gearing could have something to do with the gear shift pattern rather than the ratio.

You need them to get closer as you go up the gears. I think if you were to set the gears like that 1st and 2nd would be too close to be useful and the gap between top gear and the next one down would be too big to maintain decent acceleration.