Bringing the buttstock "up" keeps the head from canting when getting a good cheek weld. When you cant your head, it introduces a tendency to twist the rifle to fit your altered balance and perceptions. Not a big deal at 50 yards, but it will screw up your shot at 200+ yards.
Shooting from standing or seated/kneeling, you put the "toe" of the stock into your shoulder. This brings the stock up so it meets your cheek, rather than bringing your cheek down (and twisting your neck) to find the stock.
Shooting from prone, you put the "heel" of the stock into your shoulder. This is because when you shoot from prone, you are essentially pointing the rifle "up" according to your body already.
While I wouldn't recommend it for a .338 Lapua or .458 WinMag, I routinely shoot my .308 M14 the same way as my 5.56 AR-15. Toe in the shoulder for standing/seated, heel in the shoulder for prone. Lots of Garand shooters do it just fine with .30-06, also.
However, whether you put the toe or the heel of the butt into your shoulder pocket, make sure it's the POCKET. Not the collar bone. The meat of your shoulder takes the impact of the recoil. Not the fragile shoulder bones.