Skin

A Skin refers to the texture that is placed onto a player model or mob.

The skin is divided into areas that act as the surface area of the character (For example, there's the front head area, left leg area, etc.). A skin will only allow solid color; transparency is not allowed on the skin file except on the second head area, which is transparent by default. The second head layer can be used to give the character glasses, hats, or other accessories (even a bigger head).

World Textures
A skin can also refer to other textures in the game, such as block textures, item sprites, mob skins etc. A list of these can be found here. Modifying these is now supported since the Minecraft Version Alpha 1.2.2 Update on November 10, 2010.

It is worth noting that Pigmen, Zombie, and Zombie Pigmen mobs can use typical player skins (and vice-versa).

Changing Player Skins
A player can only change their character's skin if they purchased Minecraft. This is done on the Profile page by uploading a valid .png image file, which will then replace the default skin. The char.png file in minecraft.jar can also be changed and replaced, but then, only in that game the player character will appear different, and that is also the case for other people who use the default skin.

Creating a skin
Here is a zoomed-in template for creating skins.



It is also possible to preview your custom skin and edit your skin with a variety of community made skin editors.

The skin has to be 64 x 32 pixels, or else it will not work.

As of the 1.9 pre-releases and 1.0.0, all Bottom textures (including Hand and Foot) have been turned 90 degrees.

Capes
Capes are vanity items and are worn in addition to the player's skin.

Forum Discussion: http://www.minecraftforum.net/topic/648202-all-existing-cloaks-in-minecraft/

History
In October 2011, Notch renamed the cloak to the cape mentioning that the name was already wrong in the first place.

It is unknown if the Christmas/New Year capes will be given out yearly.