Here is the condenced version as I understand it:
In a two stroke, every time a piston reaches the top, there is a detonation and hence a power stroke on the way down. A four stroke only detonates every second time it reaches the top of its stroke. This means that the four stroke has hitorically needed almost twice the displacement to achieve the same horsepower.
There are many other differences in the engines (when exhaust gases are vented, when air/gas is injected into the cylinder, etc, etc), but the major difference is how often the fuel in combusted that differentiates the two engine types.
I hope I got this right. If I didn't I'm sure someone will make darn sure to correct me.
-Mark-