Strength is a measure of your raw physical power. It affects how much you can carry, and determines the effectiveness of all melee attacks.
The ability to see, hear, taste and notice unusual things. A high Perception is important for a sharpshooter.
Stamina and physical toughness. A character with a high Endurance will survive where others may not.
A combination of appearance and charm. A high Charisma is important for characters that want to influence people with words.
Knowledge, wisdom and the ability to think quickly. A high Intelligence is important for any character.
Coordination and the ability to move well. A high Agility is important for any active character.
Fate. Karma. An extremely high or low Luck will affect the character - somehow. Events and situations will be changed by how lucky (or unlucky) your character is.
In combat, you do +10% damage against male opponents. Outside of combat, you'll sometimes have access to unique dialogue options when dealing with the same sex.
You are such a Party Boy that you no longer suffer the withdrawal effect from alcohol addiction.
With the Adamantium Skeleton perk, your limbs only receive 50% of the damage they normally would.
With the Iron Fist perk, you do an additional 5 points of Unarmed damage per rank.