Prior to the M2010 rules changes, an attacking creature without trample dealt all it's combat damage to one target of the attacker's choosing. For example, a 9/9 non trample attacking creature is blocked by three 3/1 creatures. The attacker then chooses one of the blocking 3/1 creatures to deal 9 damage to. In this example, barring any instants or abilities, the attacking creature and the chosen blocking creature will go to the graveyard when combat damage resolves.
After the M2010 rules changes, the attacker can now divide it's combat damage among blockers with or without having the trample ability. For example, a 9/9 non trample attacking creature is blocked by three 3/1 creatures. The attacker then chooses the order in which his creature will deal damage to the blocking creatures. The attacker then chooses the amount of damage dealt to each creature, provided lethal damage is dealt to each creature in order. In this example, barring any instants or abilities triggering, all four creatures will now go to the graveyard when combat damage resolves. If the 9/9 attacking creature had trample, the attacker could choose to deal the remaining 6 damage left over after lethal damage was dealt to all blocking creatures to the defending player.