A model is a representation of an object in the game world. It is the spacial structure of the object within the game space environment. Depending on the game engine, the model may have other various properties at various nodes, indicating joints, flexibility, attachment points (for holding an object) and other physical properties.
A WoW model is "3-D graphic object". Producing a workable 3-D graphics model is a fair piece of work, combining artistic skill with a good amount of coding and debugging. Because they are somewhat labor intensive to produce, models get reused for different objects, generally with a "reskinning" (recoloring) for a different look. The Wowhead website (see external links) tracks equipments using the same model.
In WoW, you do not see the 3-D model per se; rather, you see a series of 2-D renderings of the 3-D models from your point of view. If you end up with a camera point of view inside a model, including your own character, you will see the 3-D graphic model from the unskinned inside. For example, druids in bear form can see out of their own mouths when they fall into tight locations, forcing a zoom-in.
Stealth and invisibility can be accomplished by a percentage transparency of the skinning (Alpha compositing). This appears to be the technique that WoW uses, as stealthed rogues are often partially visible, and it allows the other model properties to continue to interact within the game environment.
Mobile objects, especially player characters, NPCs, and mobs, will usually have some animations, posing sequences, associated with the model. Some static objects will as well. Active spells and enchantments will usually have an animated model.
The game's physics engine defines how an object's graphic model interacts with the game world environment.
Player models in World of Warcraft are divided into pieces (also known as "geosets"—sets of geometry, so to speak) that can be toggled or swapped out. This allows for customization and is used for things such as hair, horns, and of course, equippable items. While many of the game's armor items simply apply their textures to the character's base model, there are many items that replace a section of the model with an alternate, more armor-shaped version. This gives armor a less "painted on skin" look and adds variety among different items.
Oddly, many older cloaks that had tapered and swallowtail (note: not official names) models were at some point converted to the standard rectangular model. These models do still exist in the game though, just in much smaller numbers.