The discussion of differences between the different classes of airspace usually consumes at least one hour of ground school, so a comprehensive explanation will not be possible here, but I'll give you a few pointers.
The different classes of airspace represent varying levels of restrictions and control of aircraft. Class A is the most restrictive and most tightly controlled airspace. Class G is the least restrictive and is uncontrolled.
There are differences between the airspaces in the level of separation services provided by ATC, aircraft transponder equipment requirements, VFR weather minima, pilot qualifications, and communications requirements.
Very quickly, Class A is everything from FL180 to FL600. Classes B, C and D are usually associated with airports with varying levels of traffic and Class E (in VERY simple terms)pretty much consumes the rest of the navigable airspace that is not A,B,C or D in the eastern U.S. Class G is usually found at extremely low altitudes in the eastern U.S., and extends higher up in more remote areas out west.
I have not done this topic much justice, but hopefully it's a start.
Ray
P.S. As a side note, many countries in the world have the A, B, C, D, E, F, G classification system, however the use of those classes varies widely i.e. just because Class A is everything from FL180 to FL600 in the U.S. does not mean it's the same way in other countries.