A very basic answer would be that the blades of the wind turbine rotate when the wind hits them. The blades are connected to a box-like structure called the gear box which houses the generator.
The mechanical energy of the rotating blades is sent to the gear-box where it is converted to electrical energy by the generator , which is then passed to the transmission lines from where the electricity gets distributed. So, yeah, basically the mechanical energy of the blades rotating due to wind is transferred to the generator, which in turn converts the mechanical energy to electrical energy using faraday's law.
The movement of a conductor through a magnetic field produces a current.
The wind turbines usually have alternators which change the rotary motion into AC power which is then rectified into DC power. As the AC power from the alternator would have frequencies dependent on the speed of the wind, it can't be tied directly to the grid ( at least not easily ) so it must first be rectified into DC and then inverted to AC by a grid tied inverter. If the system is to be grid free, the DC can be used to charge batteries.
If a DC generator had been used instead of an alternator, the voltage would be dependent on wind speed limiting the usefulness of the power produced ( this was why cars abandoned generators for alternators ).
When wind turns turbines, the turbines wheels turn belts, which in turn turns a generator. Inside the generator, a coil of copper spins between a couple of magnets. This creates an electrical field, which is made into DC current. The DC current passes through multiple rectifiers that convert the DC current into AC. AC is the type of current a typical household outlet uses. Then, the AC current runs to either your home or a power plant for distribution across several neighborhoods.
Magnet, copper coil. Round and 'round.
Is there a part of the turbine in windmills that transforms the energy from the wind into electricity?