The diagram below shows a simplified version of how a wind turbine converts the kinetic energy in the wind to electrical energy.
The blades turns a shaft inside the nacelle (the box at the top of the turbine)
The shaft goes into a gearbox which increases the rotation speed
The generator uses magnetic fields to convert the rotational energy into electrical energy
The power output goes to a transformer, which converts the electricity coming out of the generator at around 700 Volts
to the right voltage for distribution system, typically 33,000 Volts
The national grid transmits the power around the country

Turbine Diagram
(Information from bwea)