With a 1:10 twist .308 you will be able to shoot the longer (usually heavier) bullets, up to (probably) the 220gr. I'd start with 168gr and work up.
Rifle barrels have lands and grooves (rifling) spiraling down the length of the barrel to spin the bullet and stabilize it. The "twist rate" is how many inches it takes the rifling inside the barrel to complete one full spiral. That translates into how many inches of travel it takes for the bullet to spin one revolution. Longer (usually heavier) bullets need to spin faster to be properly stabilized and so need a "faster twist" barrel.
For reference, a 1:10 twist barrel spins a bullet one revolution in every ten inches of travel.
