I guess at first the concept of turning 2.5V-5VDC into 100-230V seemed like generating more output than the input: something that is impossible. So how can an inverter generate more voltage from a smaller input voltage? Would it be correct to visualize this as a circuit that buffers enough voltage up to 230 and then deliver it at a fraction of the original current so the overall power the the same?
There are lots and lots of ways of bumping up voltage. As you say, the current will always be less, so that the power will always be less, maybe only slightly less, after the conversion. It isn't unusual to increase voltage. Camera flashguns do it, as do car ignition systems. The power grid is generated at moderate voltages, maybe 30,000 V, and sent down power lines at 250,000 V to 500,000 V.
There are also lots of ways of looking at voltage increasing devices. Look at force increasing devices, like car jacks. I can't lift my car, but with a jack I can. The handle of the jack travels much further around and around than the car rises.
Some converters use inductors. They work a bit like a hammer. To drive a nail, a large force is needed, more than you can get by shoving. So you accelerate the hammer over a distance, maybe 6 inches or so, and the hammer stops in a much shorter distance, maybe thousandths of an inch, and it takes a lot more force to stop the hammer in such a short distance.
You can't change the current in an inductor instantly. A low voltage increases the current in the inductor, slowly, over a long period of time. Then a switch opens and the current is stopped very quickly. The big voltage that stops the current quickly is generated by this, like the big force from the hammer.
What can make it difficult to understand, is that in many applications, the "long period of time" that I referred to is a few microseconds.