This page here is to give you the low down on all you need to know about this particular item. Mostly why it is valuable and why I felt like pointing it out to you. The only items that get their own pages like this are ones that you should definitely be looting and ones that require "other" explanation other than just vendor it.
For each of these items there are two methods of selling them, the quick and cheap way which is through barter. Type /bar or if you mouse over an item in your inventory the hotkey for bringing up the barter window on an item is Alt + Shift + left click.
The other method is through the The Bazaar. To bring up the Bazaar it is Control + Shift + Left Click. Check the value of the item in both to determine which you'd like to sell it in. Keep in mind that in order to run a trader you will need a Gold Account. Also keep in mind that if you sell in The Bazaar you'll almost always net a MUCH larger price than to a barter.
What are Briny Essences used for?
Briny Essences are the TDS version of Dreadmotes. Or, if you're familiar with TBM they have an item very very similar to the Briny Essences, called essence of life. They are much more common but the downside is they require the TBM X-pac to use. So, if you're FTP you have to still use Briny Essences. At least until the expansion after Empires of Kunark.
If you are unfamiliar with any of this, Briny Essences can be used to give you Rank 2 spells for your class.