What is the purpose of having two coils in a tranformer? I have been learning about electricity send through long distance from the power companies to people's homes. I know that power is initially send from a power company to a transformer in high voltage, so to reduce current, which then reaches another transformer nearby people's home where current is then increased by using step down transformers. However, what I don't get here, is why do each transformers have two coils? Why can't you just work with one coils or wire where direct current with high voltage is send from power company to nearby substation, where there voltage is then decreased to increase the current that flow into people's homes? The idea of having two coils in transformers just seems redundant to me. 
Edit: After, somebody pointed out that the questions is not clear, my question in short is why does transformers need two coils? Why can't it do the same job, or varying voltage and current, with only one coil, where each coils with different number of coils and in different stations, induce each other?
 A: You can make a transformer with only "one coil". It's called an autotransformer.
However for high voltage power distribution this would have serious safety issues, because the "low voltage" (110V or 240V) household supply would be connected directly to the "high voltage" wiring, and any faults such as a disconnected neutral or earth wire might be fatal, or start a fire because the "low voltage" house wiring was not designed to be safe at a much higher voltage. (Of course it could be designed to be safe, but the cost would be much higher, and every electrical appliance would also have to be redesigned.)
Also, when the voltage is reduced by a transformer, the current is increased in the same proportion. Therefore the low voltage winding is usually made from thicker wire than the high voltage. Joining two different wire thicknesses in the middle of a "single winding" rather defeats the point of having a single winding - you might just as well make both ends of the join accessible, and have two separate windings.
Autotransformers are useful in some low power and low voltage applications, like electronic oscillators - for example the Hartley oscillator circuit - or where the difference between the primary and secondary voltages and currents are fairly small, for example transforming 120V to 240V.
A: Your question is about power transmission but transformers are used in all kinds of applications from tiny little high frequency ones which might have only half a coil with a tap at 1/8th to complicated ones in power supplies of equipment with a dozen coils ! Time is too short to give you the full transformer lecture but the answer above (@alephzero) generally covers the point about electricity distribution transformers. I'll add a bit more..for reasons of economy a distribution system from generating station to home does not want to have too many intermediate transformers so the turns ratios are often large. E.G A primary voltage of 11kV and a secondary of 415V. Around 25:1 . So for 100A in you will be running 2,500A out. Thickness of coil wire somewhat different you see. Another reason , in power distribution, for keeping the two sides of the transformer electrically separate is due to the way fault protection works. You need a fully isolated (i.e. 2 coil) transformer to ensure the 11kV network fault protection works independently to the 415V system, ditto all the way up 33kV / 66kV / 132kV / 275kV networks and finally the generator output. Transformers (with 2 unconnected coils)  isolate the electrical systems on either side.   
