The Ender Chest is a special Chest added by the Ender Storage mod. Each chest has a special code represented by the three wool pads on the top of the chest. Chests with the same colour code will share the same inventory. If there is more than one Ender Chest on a map, whenever it is opened the other Ender Chests display the opening animation as well. Should an Ender Chest be destroyed, its contents will not be destroyed, only "stored" inside that chest combination.
Note that the colour of the wool will determine the original colour of the Ender Chest: White Wool will give a default color of 3 White, Red Wool will give a default color of 3 Red, etc.
Each of the three colour pads located on the chest's top face can be recoloured by right-clicking a dye on the pad. Note: the dye will be consumed. Indigo Dye will not work as a valid dye, as they come from different mods; you must use Lapis Lazuli to dye Ender Chests blue.
Since there are 16 dyes to choose from, and you can use the same colour dye on more than one pad, in total there are 4,096 (16*16*16) possible colour combinations. This makes it very unlikely (but not impossible) that you will pick the same combination as (or have your code guessed by) another player. It would take a significant amount of time and dyes for a player to systematically check all possible combinations in order to raid your chest. Be sure not to use solid colors on SMP servers, as this makes your chest an easy find.
As they are made of obsidian, Ender Chests are mined using a pickaxe. You cannot change the code or break a chest that is currently open.
Ender Pouches can be "linked" to Ender Chests by right-clicking an Ender Chest with an Ender Pouch. More than one Pouch can be linked to one chest, but not the other way around.
Ender Chests v.s. Teleport Pipes
An Ender Chest is worth approximately 7424 EMC in materials, this makes it a better choice than using Teleport Pipes, as it is slightly cheaper than the 8192 EMC per teleport pipe. Ender Chests are also more reliable than teleport pipes because teleport pipes have bugs (that will crash your client/server if they occur). They also allow inter-dimensional storage, in-between the Nether and the Overworld. However, there is a very specific bug that may occur with ender chests. With a sudden power loss to a server, ender chests may glitch, and cause the server to crash upon restart. This glitch may revert chunks to their state before being edited(same as the seed).
You can take a chest with you to the nether, place it, put your nether ores and glowstone safely within as soon as you mine them, and empty your inventory without having to return all the way to the portal. You may also use enderpouches (remember to change their colour) (Note: an Alchemy Bag also works.)
It can be used to share items between multiple bases. You can store all the mine carts for your railway stations in the one chest and have them accessible from any station. You could have a public food chest, and everyone on the server could access it at the same time.
The Ender Chest coupled with the Ender Pouch and Buildcraft Pipes can be used to make a player's inventory infinite. When you place items in an Ender Pouch, the items are also placed in the linked Ender Chest. By connecting a wooden pipe and engine to the Ender Chest, it will automatically take the items out of the chest/pouch and into whatever storage or sorting system you created. Literally giving your inventory an infinite scope as long as you add items to the pouch slower than your engine takes them out. This infinite inventory solution is useful if you are mass mining blocks--ore, stone, dirt, sand, etc.--and don't care whether or not you keep them in your inventory. There is a comparison between this method for obtaining infinite inventory and Equivalent Exchange's method on the Ender Pouch page, entitled "Ender Pouch v.s. Alchemy Bag".
As said in "Ender Chests v.s. Teleport Pipes" category, Ender Chests can be used as a cheaper and more reliable alternative to transport/teleport pipes which doesn't cause lag like a long chain of transport pipes does.