They are talking about increasing the size of the cylinder bore (diameter) in the engine block, then getting pistons to fit the enlarged bores. The "quality" of the piston is a matter of choosing the correct piston for the proposed use and desired reliability (Eutectic pistons (a type of cast piston) are cheaper, usually weighs less, and are well suited/reliabie to less extreme engines. Forged pistons are more expensive, weigh somewhat more, and will be better suited/more reliable in more extreme engines, or those using forced induction (turbocharging, supercharging) or nitrous (nitrous oxide, sort of a chemical form of forced induction). The choice of piston really doesn't do anything in terms of performance unless it raises the compression ratio.
There are a few ways to increase compression ratio (static compression ratio). Special pistons could be used, the combustion chamber size can be reduced (using closed chamber heads vs. open chamber heads, and shaving either the cylinder heads or the engine block). Our cars generally have a rather low compression ratio at about 8:1; raising it to 9:1 or 10:1 will produce more power and most likely, better fuel economy. Again, specific to our engines, the cylinder heads don't flow very well in comparison to more modern head designs, which further reduces their power output.
In general, there are a number of ways to get the power up, cylinder head porting, decking the cylinder block (the pistons on our engines can be as far as .080" below the deck surface (deck surface is the surface that the heads mate to)), and using the high compression pistons. The better ways to do this, and to address a number of issues, is to get better cylinder heads with closed combustion chambers, which addressed the flow issues, and helps increase compression ratio at the same time (camshaft will need to be changed at the same time). This is what Chrysler did with the Magnum line of engines. For the most part, the Magnum and LA series engines are the same. Chrysler did completely redesign the cylinder heads, increasing compression ratio and vastly improving flow. The 318-4BBL V8 was rated at about 160 HP in our cars, the Magnum 318 was rated at 220-230 HP, although it had moved to fuel injection as well, so it may have gained some of the power increase from that change. The LA 360-4BBL was rated at 180-190 HP, the Magnum 360 245-250 HP. Much of that is improved cylinder head flow, the remainder is increased compression ratio due to the closed chamber heads.
All the ways of increasting compression ratio and flow have costs associated with them. Decking a block is a machining operation that costs money, as does boring (along with the cost of the new pistons). Putting Magnum or Magnum type heads is the cost of the cylinder heads, plus a new camshaft and associated parts (lifters, pushrods, etc.). Ideally, this would all be done together while the engine is being rebuilt, to maximize power, and to keep costs down (it costs more to try and do this in piecemeal fashion than to do it while the engine is apart for a rebuild anyway).