A prop in any of the Source games is an entity that the player can interact with, generates physical motion and/or animations. They represent all the models you see in maps and are a highly valuable addition to the gameplay.
There many different types of props in Source. You should not confuse models with props, because props are the entities that can be a model. Basically, you can say that there are only 4 props that can become an unlimited number of models.
A prop_static is a cheap prop that cannot generate physics or animations. It does has a collision model and it can block players, as well as casting lightmaps and shadows. These props will never ever move from their position in the map and can never be removed. (Once compiled, they do not really 'exist' in the map.) There are so many examples to give: A tree, a box/crate, a car (non-drivable), a bench or even a building. Even the citadel in Half-Life 2 can be a simple static prop!
A prop_dynamic is a prop that can generate animations and move between set-up points. It cannot move on its own by origin, but it can be moved anywhere at anytime by animation! It is most likely always parented to an invisible func_tracktrain (an entity that moves objects) if it's going to animate or move. Examples are the Predator in ze_Predator_Ultimate or Bahamut in ze_FFVII_Mako_Reactor. They are simply animated dynamic props (They do not really act as a living entity, nor are they npc's of any kind). Also player and zombie models are all animated dynamic models that respond to inputs given by the client. It is more expensive than a prop_static, and can also be physically simulated by outputs if desired. (thought this is not recommended!)
A prop_physics is a prop that can generate physical motion when shot, touched, run into, ...
It acts an object that is dependable of gravity and inputs. A ball as prop_physics put onto the top of a hill will roll down when it's left independent. Examples are barrels, crates, wooden stacks, but also breakable objects such as bottles, flower pots, ...
While it is a valuable addition to the game, having too much of these objects in a map can cause a severe drop in performance and easily create severe network overhead in multiplayer.
The last type is the prop_ragdoll. A prop_ragdoll is a popular entity that can generate physical motion, and has as model always a dead body, or at least a model with a skeleton mesh. While it brings more realism to the map and add an extra value to the ambience in the map, it should never be used in a multiplayer map. Generating the physical motion of a prop_ragdoll requires an excruciatly high network data because it has to produce the same position and motion for every client on the server, thus creating network overhead at unusual levels. Therefore, prop_ragdolls are almost never seen in the zombie escape gameplay. One exception is ze_LOTR_Mines_of_Moria where there are 2 prop_ragdolls at a certain part in the map. If left untouched, there should be no lag. Regardless of the above, many servers have created succesful attemps to prevent network overhead created by occasional prop_ragdolls.