How to make horsepower
It's been said countless times, but an engine (at its core) is just an air pump. It sucks the stuff in, mixes it with an ignitable fluid, compresses and combusts it, then pushes the spent gases out. Simples.
Internal combustion engines rely on the principle of "suck, squish, bang, blow" as described above. Air comes in, is compressed (with a fuel), ignited, and then evacuated. So it stands to reason if you want more power you need more air.

Adding fuel without matching the air will just make the tune rich, and the car will bog. It's air, and how the engine processes it, which is the key to making horsepower. And this is where people who say "turbos are the replacement for displacement" need to pipe down and let the adults talk.
Turbos ARE displacement. Turbochargers, superchargers, and nitrous all ram additional air into the engine effectively increasing its displacement. The engine doesn't know if it's a 2.6L or a 26L, it's just processing a volume of air being rammed into it with giddy abandon.

If you keep ramming air into your engine, it will eventually stop making power. This is where the efficiency the engine can process the air comes into play. Otherwise known as "voumetric efficiency" (AKA, "VE"), engines which can perform the suck, squish, bang and blow process with greater amounts of air will make more power. Period.
That's a universal truth about engines, so write it down.
If you want to understand VE, look up the hullabaloo created when Honda dropped the S2000 on us. Here was an NA four-cylinder making 120hp-per-litre and it was so crazy it may as well have cooked you dinner and washed your dog at the same time.

If you want to process more air in your engine, and you don't want to go through the laborious, expensive process of improving your VE by lightening the valvetrain, improving air flow, and enhancing fuelling and spark timing, then you need to take more drastic steps.
This is where you choose to make your engine bigger for increased swept volume, or decrease it and use RPM.

By increasing the bore and stroke of your engine (often called "stroking" an engine), you increase it's capacity, thereby increasing the amount of air you can ram into it (in overly simplistic terms). This can have its own drawbacks, with cylinder wall thickness, rod/stroke ratio, and more, which can affect reliability, redline, boost limits, and more.
We're into the mathematics side of engines here, as bore and stroke ratios, con rod ratio, piston pin height, crank or rod counterweight, all come together to advise whether an engine will hang together as you push its envelope.
Or you could start squeezing it hard.

The other option is to maximise the bore of the engine, but reduce the stroke. Colloquially known as a "de-stroker", this work improves piston speed by reducing the length a piston has to travel through the cylinder bore. This then allows you to (theoretically) spin the engine faster.
In *VERY* general terms, increasing an engine's ability to RPM has the effect of increasing the amount of air you can jam into it.
Look at the 9000rpm, 6L V8s used in NASCAR which run a bore/stroke ratio of approximately 106.3mm (4.185in) by 83mm (3.25in), compared to a 6L LS that revs to only 7000rpm and uses 101.6mm (4.00in) by 92mm (3.622in) bore/stroke.

All engines are a compromise, in terms of size, weight, RPM, and so on. And so whether you stroke the engine out, or make it rev like a Van Halen guitar solo, you're going to find there will be a point the engine won't work any better by going further.
You'll also have to pick what you're using the engine for. There's no point in putting a super-fast-spinning, lightweight high-RPM combo into a big, heavy daily driver, while a time attack car isn't served that well by a low-revving torque monster.
But, the one thing which doesn't lie is that an engine's ability to pump air controls its ability to make horsepower.
