Pod or capsule is a type of a spaceship that makes players in EVE stand above the normal NPC characters (also it can be inferred from storyline that there are NPC pod-using characters). A pod is designed to 'go inside' a ship - in terms of storyline, it is "put" inside any spaceship you use, and your body is floating in a pod.
A pod is an even more basic spaceship than a rookie ship or a shuttle; it has no slots, no cargo space or drone space, very few hit points, but allows interstellar travel (it can access warp gates) in emergencies. It is slower than a shuttle but has an even smaller signature radius.
If your ship is destroyed, you always reappear in the (escape) pod; the same happens after you self-destruct your ship. You can self-destruct your pod; if your pod is destroyed you are podded (your clone is destroyed and its implants lost; another clone of yours is awakened on the station registered as your cloning facility). Note that NPCs will never target your pod (which makes it possible to scout some sites in it safely; on the other hand pods cannot access many acceleration gates).
If a character is deleted, his pod used to be discarded to the hangar of a player corporation he was a member of (if any). It needs to be verified it is so after Trinity. In the past those pods could be traded on the escrow market as a form of curio (they are worthless in game as you always own one). The Escrow market was replaced by contracts and at least since Trinity pods cannot be contracted or sold via traditional market; they cannot be reprocessed; it needs to be tested if they can be traded between players on the same station.
In the Apocrypha.5 update the pod was changed to include one high-tech looking thruster and a more streamlined shape.