Max Magicka - increases your magicka pool, increases damage on your magicka costing spells
Max Stamina - increases your stamina pool, increases damage on your stamina costing skills and light/heavy auto attacks
Max Health - increase your health pool
Armor - increases damage mitigation vs melee attacks/physical attacks (many class skills that cost magicka but have melee animations use armor for damage calculation)
Spell resist - increases damage mitigation vs spells/magicka costing aoe effects and projectiles (non melee)
Magicka/stamina/health recovery - the amount of a certain resource you will recover every 2 seconds while in combat (recovery rates are higher when out of combat, not reflected in your character screen)
Weapon power - increases damage of skills that have their damage calculated via weapon damage, these are most weapon skills, almost no class kills (there may be one or two in a class I don't play so I won't rule it out), easy to increase by upgrading weapon
Spell power - increases damage of skills that have their damage calculated via magicka, a complicated formula that involves the level of the skill with max magicka, but generally accounts for half of the damage multiplier on magicka based spells, only way to increase base spell power is through enchantments, set bonuses, buffs
Weapon critical - chance for critical strike with most stamina based skills AND melee animation class skills, appears to be at a threshold of 8m for ranged vs melee
Spell critical - chance for critical strike with most magicka based skills AND magicka weapon line auto attacks
I'm doing this while not at a computer, if I forgot a stat in the character screen let me know! Also if there's another stat not listed someone is curious about, please ask! And don't hesitate to correct me if you're 100% sure I listed something incorrectly