Stones are used to make your equipment stronger. 

 
RedStone = This is the rarest and most valuable stone.  It will upgrade your equipment’s quality (A refined ShellBreakSword would be upgraded to a unique ShellBreakSword).  Low success rate.

VioletStone = This stone will upgrade the level of your equipment (Ex: A level 71 ShellBreakSword would be upgraded to a level 75 SteelSword).  Medium success rate.

 
YellowStone = This stone is used to endow a bonus to your equipment (A ShellBreakSword(+1) would be upgraded to a ShellBreakSword(+2)).  50% success rate.  When unsuccessful with the yellowstone, the item will lose (-1) bonus unless the item is already at a bonus of 0.

 
Super RedStone = This stone will upgrade the quality of you equipment.  100% success rate.  This stone can only be obtained from Joans at Market (73,106) by trading 20 RedStones for it.

 
Super VioletStone (yes it is the yellow one) = This stone will upgrade the level of your equipment.  100% success rate.  This stone can only be obtained from Joans at Market (73,106) by trading 15 VioletStones for it. 

Super YellowStone (yes it is the violet one) = This stone will endow a bonus to your +7 and +8 equipment (ShellBreakSword(+7) would be upgraded to ShellBreakSword(+8)).  100% success rate.  This stone can only be obtained from Joans at Market (73,106) by trading 15 YellowStones for it.