A full metal jacket (FMJ) bullet is one which has a lead or other soft metal core, completely coated in a hard metal, such as copper, gilding metal, and sometimes a steel alloy. The jacket covers the entire part of the bullet visible from the case.
Although usually full metal jacket ammuntion has a soft core, it is not always the case. The British Mark 7 .303 ammuntion had the front thrid of the inner core made of a lighter material, like aluminum or wood pulp. This caused the bullet to yaw violently when it hit its target.
Full metal jacket ammuntion also has the disadvantage that it is a heavier projectile than soft or hollow point ammunition. This means the case will need more powder, which is why full metal jacket ammuntion recoils more than other examples of ammunition. Another disadvantage is that since the bullet is more solid, it doesnt expand much, and is sometimes considered to not have enough power. In a lot of cases the bullet will go straight through its target, which explains why it doesn't always have enough power.