Can someone explain this to me?, I have come across it many times in my several years of shooting but I have never understood what it meant and how it was significant.

the Browning web site shotgun section has a nice description of these terms with a picture.

Length-of-pull is the distance from a horizontal line drawn from the front center of the trigger to the middle of a vertical line drawn connecting the heel and toe of the stock.  Some fitters measure to the center of the buttstock instead.

Drop is measured at the toe or heel of the stock and is a vertical measurement between a line drawn through the rearward extended axis of the bore and the top of the heel or the bottom of the toe of the stock.  Some gunfitters measure drop from a line extended rearward from the barrel rib.

Then there's cast-off, cast-on, toe-out and a few other esoteric measures best left to expert fitters.

Arock's description is a good one. I wanted to add just a couple of additional points.

These items are all very important for shotguns because in the field a shotgun is mounted and fired quickly. You don't have time to move your cheek around on the gun because the birds are getting away.

Length of pull is important - for example if the  LOP is too long you may catch the butt of the shotgun on your clothes trying to mount the gun.

Drop is important because it affect the position of your eye in relation to the muzzle. Remember, in a shotgun your eye is the rear sight, so if your eye is in the wrong place (too high or too low) the shotgun is going to shoot higher or lower than where you are looking.

Cast is important because this effects whether your eye is line up with the centerline of the barrel, or too far right or left of the centerline - its like windage clicks right or left on a rifle.

For home defense with a shotgun all this stuff is meaningless - but for wingshooters and clay shooters its very important that the shotgun fit the shooter.