jkeller84, First of all, WELCOME to SGW!
I'll start off with what little I DO know (or think I know). I'm not a participant in the turkey shoots held all over the place, but I've spoken with a few that do shoot in them.
Most prefer some form of shotgun that has a longer barrel and tighter chokes. The idea as I understand it, is to either clear out a target or to place a pellet as close to the center of an 'X' as possible to win.
Chokes are nothing more than a slight constriction toward the end of the barrel. The intent is to make the grouping of the pellets become smaller or tighter together.
Since you're a handgun shooter, think of the choke as helping your favorite 9mm put a magazine full into a quarter vs having them in a pie plate.
Chokes don't do quite that good a job, but they do 'control' the pattern.
Patterning is the act of seeing exactly what effect on the shot a given combination of shell, gun and choke have on the shot that is coming out of a shell. It can be done at a variety of ranges but is generally done in the 25 - 40 yard range.
The method is fairly simple, place the target at the desired range, mark an aiming point on the center of the target (generally a sheet or two of white butcher paper). Set up the shotgun on a bench rest much like shooting a rifle. Aim at the aiming point and fire.
You then draw a circle 30" in diameter (15" from the aiming point) and count the number of pellets in the circle. The more pellets, the tighter the choke is.
You can do a search here on SGW to find other discussions on patterning.
Hope this has been some help.