As the fluff text has revealed, the art of reforging items was merely lost to the centuries only for it to reappear when the developers decided to add a new feature into the game.
Here's the description in a nutshell. If you're over the hit cap, but are still wanting in the haste department then they can help you out.
You can't toss any piece of armor in there. It must be item level 200 or higher. That means level 80 epics or better. It appears that they've lost the ability to reforge low level armor over the centuries.
Let's take a look at what adjustments we'd make to Quel'Delar. As you can see at the bottom, it will cost a little over 31 gold to make changes to this weapon.
Now, you need to pick a stat that your item has, but you don't really need. It reduces that stat by about half and lets you put those into something else.
We've decided that we've got too much haste and we're in need of something else. You can see that it's highlighted the stat you're going to be changing.
This is the list of stats you can add to your items. Spirit is included, because it is essentially a modified version of MP5 now. However, we do have that new stat of Mastery available to us.
We're going to remove 36 Haste from the weapon and convert it into 36 Mastery. You can see that the Haste on the left is highlighted and the Mastery on the right is highlighted as well. Also, our new Haste rating is in red to let us know that it has been reduced. All that is left to do is hit [Reforge] at the bottom.
Now we're done. The columns have swapped on it showing our new reforged stats on the left and the original stats on the right. That's because you can only reforge a single stat on an item. After that, the only thing you can do to the item is restore it to its natural bonuses which is completely free. It's also useful if you get another item and suddenly need that stat back.
When looking at the tooltip of an item, you can now see if it was reforged or not. It will add a 'Reforged' tag above the stat block of the item, but will otherwise appear like a normal weapon.