It's the volume of air inside the cylinder.
When the piston is at full downward position (when the conrod is at the bottom of the crank shaft) the piston is at the bottom of it's stroke (bdc = bottom dead centre)
The intake valve has opened and the piston moving down has sucked in air (NA). The cylinder (if NA) was at atmospheric pressure before the upward stroke. The intake valve closes, then the piston starts moving upwards.
It's compressing that volume of air (displacing it, like if you got into a full bath, you'll displace some water, as it's not compressible, but air is) to create an explosive stoichiometric mixture with high oxygen content for the volume that air occupies.
(If forced induction (turbo or SC), the pressure before the upwards stroke will be higher than atmospheric pressure and so more air in, then the compression stroke, means more oxygen, which means you can inject more fuel and still maintain a good AFR, and that means a bigger bang, and you get more power out of each stroke)
The spark then fires roughly when the piston is at TDC (top dead centre), (how far either way of TDC is the ignition timing), and the explosive mixture ignites (it doesn't detonate, that's a bad thing), it just burns fast, that boosts the pressure in the cylinder to hundreds of PSI, and that forces the piston down again.
So in short, a 3.0L V6 has 6 x 500cc/ml cylinders = 3000cc/ml aka 3L.
The 2.8 6 cyl would have had ~466cc pots, the 3.6L would have been 600cc pots.
You can add capacity (or displacement) to an engine by either boring out, i.e, making the cylinders fatter, and using fatter pistons, or by keeping the bore the same but increasing the stroke, both give different final characteristics, but increasing the stroke would mean it'd need a different crankshaft and a lot more work which is why boring out is the simpler job.
Suck squeeze bang blow.
