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Strength is a measure of how strong you are. It primarily affects your fighting ability in terms of how much damage you can deal out when you hit. Strength can also play a major role in Strength-based skills such as climbing.
Agility is a measure of how nimble you are and how quick your reflexes are. In combat, it's very important as it affects how likely you are to hit your opponent or dodge his or her attacks. Agility can also affect how fast you are at running and other skills in which Agility is important.
Leadership is a measure of how well you lead others. High Leadership skills can result in people following your orders or listening to your advice during battle. It can also grant you additional options in conversation.
Intelligence is a measure of how educated you are through formal training or from reading books. High Intelligence can allow for additional options in conversation and give you the ability to perform tasks that require formal training or education, like using military tactics in battle.
Wisdom is a measure of how wise you are. Wisdom can only be granted through experience or learning from the experiences of others. It's different than intelligence and more of a measure of common sense. High Wisdom will allow you to notice things that others might not, and may even give you additional options to choose from.
Diplomacy is a measure of how well you do in normal conversations. High Diplomacy will make it more likely for people to see your point of view, trust you, or do what you want. Someone with high Diplomacy can usually talk themselves out of any situation.
Hidden stats:
There are several hidden stats within the game. Choices you make throughout the game may influence hidden stats. Luck is one example. Luck can affect all other stats in ways you may not be able to predict.
Crossover Stats:
At times, stats can complement each other when it makes sense. For example, Strength and Diplomacy may be used when you're trying to intimidate someone, or Intelligence and Agility may be used together when you're trying to feint during an attack or perform a complex fighting maneuver.