You know those spray guns that go on the end of a hose? Where you can adjust from a fine spray to a single stream? Chokes are kinda like that. They control how fast your shot disperses, to some degree.
Main chokes are:
Cylinder or Cylinder bore--essentially a straight tube. Shot spreads fairly rapidly.
Improved--Slight constriction near the muzzle to keep the shot a little tighter a little further out.
Modified--"medium"
Full choke--more constriction at the muzzle to keep the shot pattern tighter, farther out. For longer shots.
There's some rule of thumb about the 90% of the shot hitting within a 30" circle at different distances. I can't remember the details. Maybe its:
-Improved choke: 20 yards and 90% of the shot is within a 30" circle.
-Modified: 30 yards
-Full choke: 40 yards
But I could be way off. Doesn't matter, each gun and each load for that gun will pattern differently. Look up Dave McCracken's post on patterning 101 and you'll see how to determine how your gun and your load perform.
Misses are probably caused by mounting issues (how you mount the gun to your shoulder) and swing issues more than by choke. But choke could play a role. Too much choke and your pattern is too small close in. To little choke and you pattern is too wide and "holey" farther out.
Anyway, I think choke is over-rated. My buddy who's a Sporting Clays nut has a fine over/under with quickly removeable chokes. He used to play with them a whole lot--switching chokes in between stations, etc. Now he shoots the whole course with modified over modified, and cleans my clock.