What effects do SPECIAL points have on their own?

Strength - Determines carry weight and raises melee damage. Each point of Strength increases your carry capacity by 10 and give you a 10% bonus to unarmed/melee attacks

Perception - Directly affects lock picking and pick pocketing success, and VATS accuracy

Endurance - Determines Hit points and the rate AP decrease when sprinting. It's used to determine both your Base HP (80 + Endurance * 5) and HP per level ( 2.5 + 1/2 Endurance), and is calculated retroactively.

Charisma - Affects success rate of persuasion attempts and buy/sell prices, and the maximum number of settlers in settlements.

Intelligence - Determines how much experience you get. Every point gives you a 3% bonus.

Agility - Determines your max AP and affects ability to sneak. Each point gives you 10 AP.

Luck - Affects the recharge rate of the critical meter

Source