StatsFollow

If you bring up your character window in game and hover over each stat it will tell you what they do.

In brief though:

*Stamina: Increses your HP so you can take more damage.
*Strength: Increases how hard you hit things in melee, although the exact amount of atttack power per 1 strength varies for different classes I think. I believe it also increases the amount of damage you block with a shield.
*Agility: Increases your ranged attack power (bows, guns etc). Increases your chance to critically hit in melee (and with ranged too I think). Also increases your dodge chance and your armour. For rogues and druids in cat form agility also increases attack power.
*Spirit: Increases the rate at which you regenerate health and mana.
*Intellect: Increases your mana pool and chance to crit with spells. Also slightly increases the rate at which your weapons skills increase.

WoW Wiki is probably a good place to look for more accurate and detailed explanations:

1 sta = 10 hp
1 int = 15 mana
1 str = 1 or 2 ap, depending on class, increases block value
14 ap = 1 dps
1 agi = 2 ac, some melee crit and dodge chance depending on class
spi = health and mana regen out of combat, mana regen in combat after 5sec of not casting, some mana regen during casting for certain classes with talents (mage, priest etc.)

for more detail on values, see the link as mentioned by ruby.
http://www.wowwiki.com/Attributes