Transmog will allow you to alter the look of one piece of gear that you own to appear to be another piece you own. For example:
You are currently wearing Helm A, a random green drop from Twilight Highlands. You decide you'd prefer to wear the helm from your T9 set. Provided that you own that T9 helm, you can spend some gold and Helm A will look like T9.
If I remember correctly, the following conditions must be met:
- You must own the piece you want to use the look of
- The piece you are changing can only be of green, blue, or purple quality
- The armor/weapon types must match (plate can only look like plate, leather can only look like leather, 1 hand swords can only look like 1 hand swords)
- You must be able to equip both items (so if you are a level 45 warrior, you can't transmogrify your armor to look like T13)
Granted, there are a couple of other rules around transmogrifying, all of which are listed here:
http://us.battle.net/wow/en/forum/topic/3196342583
As for drop-rates, I haven't heard/seen anything stating they would do this. However, for the dungeon gear, you will be able to buy those sets from the Darkmoon Faire after 4.3 hits. They will cost Darkmoon Tickets from the looks of it.