The Transporter is a device which allows for the movement of a person, people, or objects from one location to another. It has seen usage in every generation of Star Trek, though not without some changes.
How it Works
There are several seemingly-conflicted accounts of how exactly the transporter functions.
In Star Trek:Enterprise, Captain Johnathan Archer expressed his dislike of the transport system. Though it did exist and function at that time, it seemed to be less than safe, quite like the first boiler-cars. Johnathan Archer said that he wouldn't trust it with his life or the life of his men.
In the next chronological generation, Star Trek: The Original Series, this has changed significantly. Though there are still cynics - among them the prominent Dr. McCoy - who insist that it is a "Crazy way to travel, spreading a man's molecules all over the universe.", the transporter is used widely, and we never hear mention of the ethical dilemmas involved in its usage.
By the time of Star Trek: The Next Generation, transporters are considered (like warp-drive) to be 'a proven technology'. It is even remarked by one of the bridge crew that it's "The safest way to travel." This is said despite knowledge of a number of transporter accidents or mishaps including the cloning of a transported individual, and a transfer to an alternate universe.