Hotrod's descriptions are pretty good, and "close". There are some things to clear up.
There are four "strokes" in a complete "cycle", which is why the engine is called a "4 stroke". By lengthening or shortening the stroke, the displacement (the amount of "air" moved in and out) is either increased or decreased. The length of the rod has no bearing on stroke (a common misconsception, the crankshaft is the ONLY FACTOR affecting stroke).
The "bore" is the diameter of the cylinder. It has little or no meaning to the combustion chamber, except for what does or does not "fit". "Boring" an engine will enlarge the diameter, increasing the displacement. For an average "rebuild", the bore is enlarged by .020 or .030". In olden times, it wasn't uncommon to hear "when in doubt, bore it out!". However, an overbore of only .030" is of little consequence regarding power output. It DOES provide a "fresh" bore surface for new pistons and rings to do their job as well as possible. One must usually go at least .060", and even .100" (like BBCs) to have a real effect on power output.
The displacement is fairly simple to compute. There are lots of "witch doctor" and "backyard" methods, but there's only one you would learn in a math class. Pai x R(squared) x H x no. of cylinders, where Pai = 3.14159 (3 1/7, rounded), R = 1/2 the bore and H (Height) = stroke.
For an average "production" engine, like 350 Chevy, increasing the stroke will yield more increase than overbore. Most production engines are limited in just how far you CAN bore them without getting the walls too thin. Fords aren't considered "safe" past .040". Later Olds and Chevy small blocks, same. Earlier small blocks are usually safe to .060" over, and some to .080".
These are not "hard/fast" rules. One must always measure to be sure. The cylinder wall thickness is measured by a professional machinist using a "sonic tester". $50-$75 for a V8 block, most places.
For the more popular engine families, there are many "stroker kits" available. Some are MUCH better than others. NEVER by a "kit" based on price, unless you don't plan to pound on it too hard, OR, you aren't planning to rev it higher than 5,000. The cheaper kits have cast crankshafts instead of forgings. Those Chinese-made castings are pretty weak. The one exception is the Pontiac stroker from Eagle. Because the Pontiac crank has such large main journals, they don't flex like the smaller ones. We've seen them as high as 800 horsepower without issues. (Chevy guys, doesn't that beat all? Wouldn't YOU GUYS like a crank that can take 800 HP for less than $300?)
You will, undoubtedly, hear of many "success" stories using the chap crap. Don't buy in. For every "success", you will hear of 20 failures... And usually, those promoting the cheap stuff, are rationalizing their own purchase, more than they are advising you!
We buld many a "stroker", Chevy, Ford, Dodge, and mostly Pontiacs. The small block Chevy "383" is probably the most popular, and among the better non-factory configurations. For maximum "street" power, it's hard to beat the 461 Pontiac. We routinely build 600-plus HP, 93 octane "friendly" monsters with more than 650 lb. ft. of torque, revving to about 6,200. While the horsepower numbers are not too difficult to attain with the small block, the torque numbers are nearly impossible at such engine speeds. The BBC fares a little better, but if rectangular port heads are used, drivability is in the toilet. With oval port heads, it's hard to get such efficiency on 93. It CAN be done.
We also have a few 499 Dodges out there (440-based) that are ANIMALS! One '68 Road Runner goes 10.80s all week long, on 93, with iron heads (906s, ported here) and a Comp solid roller. He can drive it to Richmond and back without worry (about 100 miles, round trip).
Jim