Strength increases the damage you do when you hit someone.
Agility affects how likely you are to hit your opponent or dodge his or her attacks.
Wisdom changes the story text, adding more detail, it even allows for additional options. It could affect what you say as well.
Leadership is how likely people are to follow your orders or listen to your advice in battle. It may also allow additional options in conversation.
Intelligence allows additional options in conversation, it affects how you character may react in certain situations and it may allow you to do more complex maneuvers in combat.
Diplomacy affects how likely someone is to see your point of view. It affects dialogue and highly effects determining success in conversation related checks.