Guild Wars 2

What does it do? Does it make your chances of getting a better item higher?

They can be used to replace a piece of equipment when inserting four pieces of equipment of the same rarity.
For example: use 3 rares + 1 mystic forge stone as a substitute for the 4th rare, to get a new rare with a chance for an exotic item (~10-20% chance).
http://wiki.guildwars2.com/wiki/Mystic_Forge_Stone

20% chance of upgraded item

they are also used to make Mystic salvage kit. When gem prices are below .93 gold per 100 gems, it’s cheaper than Master salvage kit. when they’re not, it’s only benefit is that it has 250 charges.