S.P.E.C.I.A.L. is an acronym referring to the 7 attributes that all creatures of the fallout universe posses. In Fallout: New Vegas, you allocate your attributes using a contraption called the Vit-O-Matic Vigor Tester as part of the opening quest Ain't that a Kick in the Head. You can look at each attribute in turn and there is a total of 33 points to spend on the 7 attributes, with the 1st point of each being free. There will be another chance to change your attribute allocation when you leave the Goodsprings area for the first time. Attribute rankings are from 1 (Abysmal) up to 10 (Almost god-like) with 5 being roughly average. Each level has a quirky name given to it in order to give you a rough idea of what that level of attribute signifies.
Strength will tell you how easily a cowboy totes his saddle and those bigger firearms, or how much help he's gonna be for ya in a saloon brawl.
Strength affects the skill of Melee Weapons and adds to your Unarmed damage. It is also the skill for how much salvage you can carry on your prospecting runs. If you plan on packing a lot of gear and don't want to make too many trips just to sell and offload stuff then this is an extremely valuable attribute to have. Remember that in Hardcore mode, ammo has weight, so keep that in your mind when planning your character out.
A perceptive cowboy always knows when there's a lit stick of dynamite nearby... or when a varmint's sneakin' up on him.
Perception affects the skills of Energy Weapons, Explosives and Lockpick. It also controls when you see entity markers on your compass, and adds accuracy to all of your attacks. If you want to notice sooner if someone is nearby, and don't want to be ambushed a lot, then this is an extremely valuable attribute to have.
You can't keep a good cowboy down, not if he's the endurin' type... and not if he's got a six-shooter the size of all tarnation.
Endurance affects the skills Survival and Unarmed. It is also the attribute that assigns your health points. If you are going to be a hand to hand expert you will consider this an extremely important attribute to have. If however you want to focus more on killing things from afar or social skills, then you can skimp on this attribute some. There is a hidden attribute of fatigue that is also governed by your endurance. Some weapons and poisons inflict fatigue damage instead of lethal, and if you are fatigued enough you will fall unconscious. A higher endurance affects how long you can get hit before you fall down.
You'll find there are some smooth-talkin' cowboys out there that got themselves a voice sounds like an angel's harmonica.
Charisma affects the skills Barter and Speech. It also affects how others react to you in conversation. If you want to be a smooth talker and try to avoid combat through conversation, then this skill will be extremely important to have. It also provides a percentage bonus to the armor and damage of your companions.
A smart cowboy is good at most anything, from suckin' the poison out of your rattler bite to fixin' your broken wagon axle.
Intelligence affects the skills of Medicine, Repair and Science. It also affects the amount of skill points you receive at each level, with the .5 of odd intelligence scores holding over until the next level. This can be an extremely important skill for a number of reasons: keeping yourself healed, keeping your equipment in good condition and being able to hack computers or do other science related challenges easier. The drawbacks of an extremely low intelligence score is that your character will barely be able to converse in monosyllabic grunts. This can make some quests very difficult if not downright impossible.
When a fella's in a gunfight and shoots the other guy six times before they can get off a shot, it's because that fella is agile.
Agility affects the skills of Guns and Sneak. It also affects how fast you run, draw/reload your weapon, how many action points you have and how fast they regenerate. There is no real way to measure your speed, however the higher agility the faster you will move. If you have a two-handed weapon out, it will slow you down as well, so if you are in a hurry holster it or carry a one-handed weapon. If you intend on using VATS a great deal, you will want a higher agility to reap higher action points. You will also want it for sneaking potential.
Some folks claim not to believe in luck, but when they lose in a duel you'll hear them say "That lucky son-of-a-gun!".
Luck is a very difficult attribute to completely quantify. It affects all skills to a lesser degree than the other attributes. Your critical chance is improved with a higher luck score, enemies may have more mishaps and if you are gambling, you will find that the cards/wheel/slots seem to fall in your favor more often. If you are something of a generalist, want a broader range of more equal skills and want to clean house at gambling with a minimal amount of actual skill, then luck will be your favored attribute.