What is the meaning of the word 'Pilot', as used for the first episode of a TV-show, implied here? Does it have anything to do with a smooth take-off?
According to Etymology Online, the term pilot has been used since the 1920s to mean "serving as a prototype". It is this sense that you get terms like pilot episode for a TV Show, or pilot program for an emerging technology.
If you go back further in time, there was an old sense of pilot as far back as the 1600s meaning "to guide". For example, in woodworking there is a common technique of drilling smaller "pilot holes", sometimes called "starter holes", in places where you plan to attach two objects by screw; the pilot holes guide the screw in straight and prevent the wood from splitting under the stress.
This earlier sense pre-dated the concept of manned flight by hundreds of years. However, the term pilot is not just used for the captain of an aircraft: the person who steers a ship or boat is also called the pilot, and their job is to "guide" the vessel along the correct path to avoid running aground, etc.
Most likely, the later sense of a pilot episode evolved out of the idea that this episode "guided" the TV show and got it "started" through the initial process of being picked up by the network.
A Pilot episode is like a Pilot light, a small flame that is used to start a bigger fire. If the pilot goes out, there can be no fire. If the pilot fails to get an audience interested, there can be no show. A Pilot light or burner is a well known term prior to the first use of pilot episode, predating it by 70 years.
Pilot (here) is basically considered in a way like an airplane that can be only flown by a pilot who is therefore considered as someone or something that helps taking off.
If we consider "pilot" in the tv shows pattern, it means that in order to convince a tv studio or a production house under whom that show is getting is made and of whom pilot is being shown, gives a greenlit.
The reasons of pilot are many, most of them redirect towards of how it helps to give a launch to a tv series by acting as its deal maker or deal breaker.
Watch any pilot an compare to it other episodes of the same tv show, and know the truth, which will give you the sense of what pilot means.
Typically, when a television network is interested in a potential series, they'll commission a "pilot episode." The pilot episode is a single episode that serves as a sort of test of the concept. Often, pilots are deemed unsuccessful and nothing more ever comes of them. But if the network executives feel that the pilot is a success, then they may elect to order a full series of the show.
Sometimes, the show proper is re-tooled to varying degrees compared to its pilot episode (The Dick Van Dyke Show is a classic example of this). Other times, the pilot episodes becomes the de facto first episode of the series. This is why the first episode of many shows bear the simple title, "Pilot."
According to this answer on Quora
One of the definitions of "pilot" is "1. Serving as a tentative model for future experiment or development: a pilot project." And it is this meaning that applies to a TV series. The pilot episode is made on its own as a test for whether a show might work. Then the executives at the network decide if they're going to "pick up" the show. Often, the pilot serves as the first episode, but not always. Sometimes the pilot has to be thrown out - usually due to casting issues, sometimes locations. Game of Thrones is a recent example of this.