I came across a forum posting by ‘RSE Custom Guns’ explaining what a free-bore is:

Free bore is just that, it is the area ahead of the bullet ogive in a rifle barrel to which there is no rifling, once the cartridge is fired the bullet travels freely in the barrel until the bullets ogive contacts the rifling, hence free bore.

Why add more free bore:

The case for free boring is made this way, if you have a bullet seated deeply in a rifle case, the bullet is actually decreasing case capacity which in turn lowers the over all velocity of that imparticular bullet / case loading.

By adding more free bore, the bullet is then able to be seated out further thus increasing the case capacity which in turns allows you to add more powder to the case and thus an increase in velocity, usually quite a substantial increase in velocity.

How much can it help:

Usually increases are substantial to the point of standard calibers will be within reach of magnum velocities and magnum cartridges really get to actually earn the name magnum.

More here.