This page mostly deals with information visible in the "Status" option in the sub-menu of the original FFVII.
In general, the Attack stat and the Strength stat govern the exact same thing; physical damage which that party member can inflict. The Defence stat and the Vitality stat are the inverse of Attack and Strength; they govern reducing physical damage received from enemies.
Magic Attack and Magic govern magical damage which the party member in question can inflict. Magic Defence and Spirit are the inverse; they govern reducing magical damage received from enemies.
It's probably obvious, but having an Attack of e.g. 200 does not mean you will deal 200 HP damage...
With most equippable armor, to get an idea of that party member's capacity to protect against physical damage, simply add the Defence of the armor to that party member's Vitality stat; likewise for the party member's ability to protect against magical damage, add the Magic Defence of the armor to the party member's Spirit stat.
With most equippable weapons, to get an idea of that party member's capacity to inflict physical damage, simply add the Attack of the weapon to that party member's Strength stat.
(N.B. don't forget some accessories also raise stats, take this into account)
The main exception are ultimate weapons. Ultimate weapons actually fully ignore the characters' Strength stat as well as the ultimate weapon's own Attack stat. The capacity of an ultimate weapon to inflict damage depends fully on that weapon's special property e.g. the number of enemies Vincent has killed in the case of the Death Penalty.
Ultimate weapons also completely ignore enemies' defence stats. I tested this by raising Tifa's Strength to 255. Even with Strength at 255, she hits poorly with the Premium Heart when her Limit gauge is empty.
Find out how to raise Strength to 255.
There is more than one way around this. You can alternatively equip the God's Hand weapon to Tifa; or you can keep her Limit Break gauge full, never use her Limit Breaks and use the Mug command (from Steal materia) instead of Limit (Mug won't reset her Limit gauge back to 0).
Every 4 points added to the Dexterity stat will raise that party member's Defence % by 1. 255 Dexterity therefore raises Defence % by 63% (255/4=63.75).
So a character with 255 Dexterity and a Mystile armor equipped (complete armor guide here) has a Defence % of 113, i.e. 63% from the Dexterity + 50% from the Mystile. N.B. The maximum Attack % in the game is 255% - assumedly for enemies and verifiably for party members. As such, a Defence % of 113% doesn't guarantee you will avoid suffering physical damage. However, if you raise both Dexterity and Luck to 255 each, you have an extremely low chance of suffering damage, as long as you also have a Mystile armor equipped. Note that the Dexterity stat also affects the speed at which your time gauge fills up; at 255 Dexterity, it will be fast.
The Luck stat, as far as I can tell, affects a number of things. With Cloud's Luck at 255, he seems to hit a critical every single time.
I'm pretty sure the Luck stat affects the percentage type stats e.g. Attack %, Magic Attack %, Defence %, Magic Defence %. Magic Attack % is never mentioned in the game, but I'm pretty sure it's logical it must exist; it's just hidden.
You can give a character a fair few more sources even once a stat is at 255 before the game won't let you give any more. This is probably because even with a stat at 255, it would drop below 255 with certain materia equipped.
Understanding this is a little complicated. Let's say you raised the Strength stat to 255. If you were to equip an Ultima materia on the character with 255 Strength, they would end up with only 251 Strength, as one Ultima materia lowers the equipped party member's Strength by 4. If you equipped 16 Ultima materia on the party member with 255 Strength, the Strength would drop by 64 (4 Strength x 16 Ultima materia) to 191. So the game allows you to give up to 64 more Power Sources after reaching 255. The Strength stat will still appear as 255, but in reality it will be 319. This means that Strength would stay at 255 even with 16 Ultima materia equipped, as 319 - 64 = 255.
Then Square Enix decided to have it this way for all of the 6 stats of Strength, Magic, Vitality, Spirit, Dexterity and Luck; even though it is only possible to reduce a stat using materia by as much as 64 when it's the Strength stat. There are no materia which lower Magic, Spirit, or Dexterity; and it is not possible to reduce Luck or Vitality by as much as 64 with any possible materia setup. It was probably done for programming consistency.
You will know when you've truly maxed out a stat to 319 as the game will make a "buzz" noise when you try increasing that stat; and also because you won't have less Sources, checkable in the Item part of the Menu...
One further thing of note: a party member with 255 Magic, and a Knights of Round materia equipped, will take off 9999 HP or very close to it with every hit of Knights of the Round; without Knights of Round needing to be linked to an MP Turbo materia.
Linking Knights of the Round to an MP Turbo raises the MP which KOTR uses to 255 - again, this is the maximum figure, and it guarantees you will always hit for exactly 9999 HP with every hit of KOTR.
[Peerless] can be considered a supernormal status. While in [Peerless] state, you are immune to any damage.
You can only obtain [Peerless] status in FFVII by using either Aeris' Planet Protector or Great Gospel Limit Breaks.
[Haste] is another example of a supernormal status.
[MBarrier] and [Reflect] can probably best be called paranormal statuses. They can both be beneficial, e.g. if used to reduce or reflect magical attacks. However, they can be detrimental if e.g. you cast a Cure spell and it gets its efficacy halved or bounces off to an enemy..
[Silent] and [Darkness] are subnormal statuses. They confer a disadvantage on the affected character and have no apparent possible beneficial effects. I suppose if a party member had [Darkness] as well as [Confu] then the [Darkness] status would help stop the party member successfully hitting other party members; but really, it gets a bit overcooked thinking that far... More useful might be if you set up a party member to absorb Poison elemental damage, and then cast Poison on that party member; it would work similar to Regen.
[Berserk] is maybe best looked at as an abnormal status. Generally it can be both useful and detrimental, but perhaps not as heavily so as the paranormal statuses above.
Elements can be applied to a party member's Attack or Defence. To apply an Element to a party member's Attack, equip a Magic materia of an Element (e.g. Fire or Earth) linked to the "Elemental" Support materia in the party member's weapon.
To apply an Element to a party member's Defence, link a Magic materia to an Elemental materia in the party member's armor.
Certain armor and accessories also provide Elemental protection, e.g. an Escort Guard or a Water Ring.
A Level 1 Elemental materia in armor will halve any Elemental damage of that type inflicted by an enemy. A Level 2 Elemental will nullify damage of the linked Element. Level 3 or 4 will cause the Element to be absorbed, meaning it will actually heal that party member.
If applying an Element to Attack, it really depends on what enemy you are up against. Enemies can also halve, nullify or absorb damage from an Element...but enemies can also be weak to an Element. So if for example you use Ifrit (Fire Element summon) and the enemy is weak against Fire, Ifrit will deal double damage.
Which brings me to my final point - Magic, Summons and Enemy Skills can all be based on one or more Element...try and take advantage of this while using them!
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