The barrel throat is that portion right in front of the mouth of the case, where the bullet fits when the rifle is loaded. It gets a major blast of hot gas every time the rifle is fired and that affects the steel of the barrel. This is worst in rifles loaded (or overloaded) to gain high velocity, but it happens in all rifles.
As it becomes worse, throat erosion eats away at the lands in the barrel throat until the bullet gets a poor start on its way, tending to slew and skid as what is left of the rifling tries to grip it. While the bullet will eventually "straighen up and fly right" to some extent, its accuracy will not be the same as one with a good sendoff.
A brand new barrel would run 0-1 on a T-E gauge; a shot out barrel would be a 10 (in this case, the worst; we are talking about barrels, not women). A barrel gauging 3 would be in good shape; a 5 would still have a lot of life left and be perfectly serviceable.
Throat erosion should not be confused with rifling wear at the muzzle, caused mostly by cleaning rods. In a some rifles, muzzle wear can be corrected by back boring (drilling the bore to a larger size for 1/2 " or so), or cutting off the barrel to good rifling and recrowning. But that can't be done on an M1, since the M1 needs that barrel length to provide enough pressure through the gas port to function. The only practical way to correct muzzle wear on an M1 is a new barrel.
Jim