The four nacelles of a Constellation-class starship.
The nacelle is an outboard structure on starships which houses the warp coils. The warp coils create a subspace displacement field, which warps the space around the vessel allowing it to "ride" into subspace, to provide the ability to travel faster than the speed of light. (ENT: "Cold Front")
The warp coils are fed by plasma conduits from the vessel's warp core reactor assembly. Nacelles are usually separated from the main structure of the ship because of radation generated by the nacelles, when at optimal levels, could be deleterious to the safety of ship and crew. On Federation starships, nacelles are usually grouped in pairs only for maximum efficiency, and separated from the ship by large pylons, and usually house a Bussard ramscoop at the fore end for the purpose of collecting hydrogen fuel to replenish the engines.
A nacelle's interior also includes a small control room, accessible in nominal conditions by a Jeffries tube that permits maintenance and monitoring of the system's operation. (TNG:"Eye of the Beholder")
Most vessels typically have two nacelles. Experience has shown that having two nacelles is the optimal configuration for vessel control and efficency. (TNG Technical Manual) But it is not unheard of for vessels to have additional nacelles. One example would be Federation Constellation class starships - which have four nacelles.
Nacelles also have a seperation system in the event that the ship is damaged and unable to retain the nacelle safely on the pylon. On Galaxy class starships explosive charges seperate the nacelle and lift it up and away at 30m per second. If a nacelle is lost during warp flight, it can tear the ship apart as the loss of a nacelle would cause different areas of the ship to travel at different speeds. Even at sublight speeds serious impacts from weapons or other objects can spell disaster for a ship because of a feedback of energy throughout the vessel.
See also: Warp drive