Why does galvanometer show the deflection due to movement of conducting wire up and down?

When the conducting wire is continuously moving up and down there is change in magnetic flux linked with closed circuit and by the Faraday's law induced current is produced and galvanometer deflects. 

Galvanometer, instrument for measuring a small electrical current or a function of the current by deflection of a moving coil. The deflection is a mechanical rotation derived from forces resulting from the current.The major significant difference between ammeter and galvanometer is that ammeter shows only the magnitude of the current. Whereas, the galvanometer shows both the direction and magnitude of the current.A moving coil galvanometer works on the principle that a current-carrying coil placed in a magnetic field, experiences a torque. The coil springs along with the radial field ensure the deflection to be proportional to the strength of the current.

The SI unit of the figure of merit of the galvanometer is Ampere per division. The figure of merit can be defined as the current required to produce unit deflection on the galvanometer.

A galvanometer is an electromechanical instrument used for detecting and indicating an electric current. A galvanometer works as an actuator, by producing a rotary deflection of a pointer, in response to electric current flowing through a coil in a constant magnetic field.First we calibrate a galvanometer to detect the presence and the direction of a current.  When current enters the terminal on the right hand side of the galvanometer, the needle deflects to the left.

A galvanometer is a device used to detect feeble electric currents in a circuit. ... The deflection is proportional to the current passed. The galvanometer coil has a moderate resistance (about 100 ohms) and the galvanometer itself has a small current carrying capacity (1 mA).