The original explanation of the stats is credited to Shadow Cloak (or is it Tyr? can't remember >_<); this is in my own words, however.
Strength: This plus the power of the weapon = Attack Power
Stamina: This plus the power of the armor = Defense
Agility: This minus the weight of the armor = Vigor
Wisdom: This is your ability to resist magic
Luck: Alters probabilities; need a lot for it to make any difference
Attack Power: Major factor in determining the damage you can do with a normal attack and certain specials
Defense: Major factor in determining the damage you take from a normal attack and certain specials
Vigor: Determines order of action in a round; highest vigor goes first, and works on down. In case of monster/character ties, character will act first.
Condition: Range is Ill, Poor, Okay, Good, and Super. The better the condition is, the more likely a character is to make a critical hit (via normal attack or magic), dodge an attack, and resist attacks that are a "succeed or fail" sort of thing. Condition changes over time. It can be raised to Super by a Condition-Up or by the Pub-carpenter. It can be reduced to Ill by a Curse.
Guts: The higher this is, the more HP Ryu can recover with his Guts special. It can also enable a character to get back up after being killed; very rare though (odds are less than 1 in 4 if Guts is maxxed out).
Strength, Agility, Stamina, Luck, Wisdom, and Guts can be raised by assorted Etc. items and PARs. All but Agility have a max value of 255; Agility has a max value of 511. The highest number of flames that will appear for Guts is 7. Shaman bonuses are determined by multiplying these by a percentage and adding the result to the appropriate area. Luck and Guts cannot get shaman bonuses.
Poison: Afflicted characters lose 1 HP with every step when traveling the world. Can be inflicted by the Poisen attack (damages and poisons one character) or by Poison Breath (affects the whole party), and one or two specials.
Zombie: When contracted, character will change coloration. Character will be fine for the round contracted and for the next round. Unless it has been cured, character will turn into a zombie and start attacking the party the next round. Character has effectively died. Can still be cured after complete zombification; is automatically cured if zombification is not complete when battle ends. Can afflicted by the Zombie attack (damages and afflicts one character), or by Rot Breath (affects the whole party).
Sleep: Character will not act until physically struck. Cured automatically if battle ends. Can be afflicted by Sweet Breath (affects the whole party) and by a special. Magic attacks will not wake up a sleeping character.
Curse: Extra-special spell; reduces Condition of a single character to Ill (character is effectively unable to make critical hits, or dodge/resist attacks).
A Shiny Bracelet or the appropiate Etc. items protect from these ailments.