The forcing cone is the area in the barrel from the front of the chamber to the actual bore. It is tapered and (as mentioned in the previous post) is the area in which the shot, having been expeled from the shell, is forced into the bore. The longer, and less drastically angled, the forcing cone is the less damage is going to be done to the shot column and the less force is going to be spent in that area (which should reduce felt recoil).
Backboring is the opening up of the actual inside dimension of the barrel's bore. There are a couple different formulas for the optimum dimension. Which you choose depends on who you believe has the right numbers. The late Stan Baker was probably the foremost proponent of this practice, but it has gained enough respect that even the new manufactured guns have started to come out with barrels that are built to the wider dimensions.
It should be noted that if backboring is done correctly the chokes will also need some work. Remember that choke is measured in terms of constriction, and if you change the diameter of the barrel without changing the choke you in effect increase the amount of constriction, and therefore the choke.