A voltage is induced in the coil, and it is this voltage which pushes electrons around the coil and through the external circuit. In order to induce a voltage in a conductor, the conductor must cut through or cross the magnetic flux lines.
So if you are wearing a gold watchband, running cross-country from north to south will not induce a voltage in your watchband because you are moving along a magnetic line of the Earth (these imaginary lines are drawn around the Earth from the North Pole to the South Pole). But if you run east-west you are cutting across the Earth's magnetic lines and causing a voltage to be induced in your watchband (providing you orientate it to best effect).
Even so, the voltage is too small for you to measure.