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This is some extra information that I manage to gather from Taiwan SRO guide. Its on the premium guide, so I would assume that the information is correct.

Each Weapon/Armor/Protector/Garment/Accessories will have a Phy. and a Mag. Reinforce Value. According to the guide, Phy. and Mag reinforcements are just a set of useless numbers if Elixirs are not used on it.

Lets look at this picture (sorry that its a Taiwan Version)

http://img220.imageshack.us/my.php?image=110ru8.jpg

Reinforces of the weapon are as follows:
Physical Reinforce of the weapon is 53.5% ~ 63.5%
Magical Reinforce of the weapon is 94.0% ~ 115.0%

It basically means that with every Elixir used on the weapon that is successful, it will add Physical Damage of 5 ~ 6 and Magical Damage of 9 ~ 11 on it.

The picture shows a b4 and after the Weapon (+1) itself. At (+1) its Physical Damage was increased by 5 and Magical Damage by 10.

Hope this helps. Correct me if I am wrong. Cheers.

For the last time, reinforce has nothing to do with elixers.

It is part of the calculation used to determine your final stats

Mag att=(int*reinforce)+mag att
Phys att=((str*reinforce)+phys att)(1+weapon mastery/100)

The extra factor for physical attack is the bonus damage from the master level. This also applies to magical attack, but because you can use multiple types of magic masteries with the same weapon it is not reflected on the character screen (screen that lists stats, job exp, etc). It is however still counted in the final damage when you hit something.

For armor this works in a similar way, but I haven't seen the equations that can be confirmed yet.

Let me ask this: if the amount elixers added was dependent on reinforces, how do they determine it for accessories?

ive, never, pay enough attention on that. dont mind that much..