They make your equipment slightly stronger.
Weapon elixers for weapons.
Protector elixers for your clothes.
Shield elixers for your shields.
Accessory elixers for your jewels.
On your equipment it says a degree like 1st degree, 2nd degree etc, what you do is you buy a lucky powder from the jewels npc's that correspeonds to the same degree as the equipment you want to alchemy.
You then press Y to open the alchemy box, click the tab at the top to change it to less boxes and then u drag your equipment in along with the elixer and the power and click OK or whatever it says.
Then you either get a succeed or a fail, you can keep adding them in, usually +3 is enough for most things, they do fail a lot though.
Just gives slightly better stats.
http://www.silkroadforums.com/viewtopic.php?t=88
See this thread also.
You know it, it's true 
..nice one.. 
