The following is a copy of a post I made on 12/28/04 in answer to a similar question:
Here's a simplified way of understanding what choke, or barrel constriction, does in a shotgun: On your garden hose at home chances are that you have an adjustable nozzle that will change the shape of the stream of water issuing from it from a wide cone-shaped pattern to a sharp stream. Choke in a shotgun works in a similar manner. By constricting (or not) the end of the barrel, the shape (and hence, the density) of the emerging shot pattern is changed.
The degrees of barrel constriction are measured in thousands of an inch and have been given names. The major ones are: Cylinder, Improved Cylinder, Modified, Improved Modified, and Full. "Cylinder" means no constriction, while at the other extreme "Full" means a constriction of about 30 thousandths of an inch smaller than the bore diameter. The intermediate ones provide increasing degrees of constriction as we move from Cylinder to Full.
When you go to your local gun shop you will see a wide variety of shells for your shotgun. The basic variables are shot size (the smaller the number, the larger the diameter), quantity of shot, and amount of powder to propel the shot. At various degrees of choke, each of these shells will deliver X-percentage of their total number of shot into a 30-inch diameter circle at a distance of 40 yards. Typically, these percentages are: Cylinder 25-35%, Improved Cylinder 35-45%, Modified 45-55%, Improved Modified 55-65%, and Full 65-75%.
This gives us a basic framework for understanding the best combinations of shell and choke for each shooting situation. For example, if you wanted to kill a turkey, Winchester recommends size 4, 5, or 6 shot used with a full choke. Why? Turkeys are wary birds, hence they are generally shot at a distance. They are also heavy and heavily feathered so you want to hit them with the maximum number of larger shot to insure a clean kill. The full choke will deliver the greatest percentage of this shot (in the sizes mentioned) at the greatest distances. On the other hand, suppose you want to kill a quail: Winchester recommends size 7.5 or 8 shot used with an improved cylinder or modified choke. Why? Obviously, quail are smaller birds, hence the need for smaller shot (you want something left to clean and prepare for the table!). Also, quail are typically killed at a closer distance, but because they are agile you want a broader pattern with as many shot in it as possible to insure a clean kill.
This is an oversimplification of a rather complex concept; however, I hope that it will help you to understand the basics. I recommend that you obtain a copy of Winchester's (or any of the other manufacturers') Ammunition Product Guide (available from your local gun shop) and study its Shotshell Game Guide. This guide will detail the shot size and choke recommended for various types of game.
Good luck and good shooting!
