SPECIAL is the system created for Fallout to define your character's traits. SPECIAL is the acronym for the traits: Strength, Perception, Endurance, Charisma, Intelligence, Agility, and Luck. Stats range from 1 to 10, with 5 being "average", though values from 4-6 would all be in the range of human norm. Anything above 6 or below 4 is going to be a noticeable, obvious trait of your character.
Strength is your character's muscle mass. How hard you can swing or hit, how much you can lift, and, to an extent, how much punishment you can take are all based on Strength.
Perception is your character's senses. How far you can see, how accurate your vision is, how easy it is for you to notice details are all based on Perception.
Endurance is your character's health. How resistant to radiation, poison, disease, fatigue, and injury are all based on Endurance.
Charisma is your character's presence. How people react to you, your looks, your force of personality, your animal magnetism and first impressions are all based on Charisma.
Intelligence is your character's smarts. How well-spoken you are, how intuitive and insightful you are, and how quickly you can learn are all based on Intelligence.
Agility is your character's control. How poised and balanced you are, how light on your feet you are, and how steady and precise your hand and aim are all based on Agility.
Luck affects everything a little bit. It's sort of ephemeral, but all things equal, the lucky fellow will always win. With an excess of luck, one can even make up for mediocrity. A lucky character has slightly better odds, all other things being equal, than an unlucky character.
All stats start at 5, and can be adjusted on a one-for-one basis. In addition, you have 5 additional points to allocate to stats as you wish.
Every character will pick three "Tag Skills". These are the skills you excel at, regardless of SPECIAL stats. This can raise you far above average, or put you on average in something you would otherwise lack. Luck has a minor effect on every skill.
A skill name is listed, followed in parenthesis (like this) by the stat that is primarily associated with it, and then a brief description of the skill:
Barter (Charisma). Skill at trading and haggling. High Barter means you can "drive a hard bargain".
Energy Weapons (Perception). Shooting things with lasers and plasma weaponry. Any weapon that doesn't use bullets or explosives.
Explosives (Perception). Using things that blow up. Grenades and grenade launchers, dynamite, mines, planted charges, missile and rocket launchers.
Guns (Agility). Shooting things with bullets. If it uses bullets as ammo, it's a gun.
Lockpick (Perception). Picking locks. Opening things others don't want opened.
Medicine (Intelligence). Patching people up. Proper use and handling of drugs.
Melee (Strength). Hitting things with sticks, pointy or not-pointy, with metal bits or without metal-bits.
Repair (Intelligence). Fixing things, especially mechanical things. Also cobbling things together or modifying existing technology.
Science (Intelligence). Computer hacking and general knowledge. Making drugs, recycling pre-War energy sources.
Sneak (Agility). Staying unseen. Stealth, legerdemain and prestidigitation.
Speech (Charisma). Convincing people. Swaying folks to your side with reason or (more usually) rhetoric. Also, how believable you are, whether lying or not.
Survival (Endurance). Living off the world. Finding good food to eat, good water to drink, safe places to sleep. Preparing those for others.
Unarmed (Endruance). Punching stuff, with or without gloves or other mechanical assistance.
Besides your stats and your tag skills, don't worry about anything else.