It is best if you read the page on the Magnetism first.
When a current is passed through a wire which is suspended in a magnetic field, the wire will move. The direction of movement is determined by the direction of the field and the direction of the current. The speed of movement is determined by the strength of the field and the amplitude of the current.
This principle is used in the electric motor to produce rotation. It is also used in the loudspeaker where varying speech currents through a coil, suspended in a magnetic field, causes movement of a cone, resulting in sound pressure waves.
The moving coil meter uses the same idea. When the meter is connected to a circuit, current passes through a coil. The coil is suspended in a magnetic field, and rotates when current passes through it. A pointer fixed to the coil indicates a value on a scale.
The Electric Generator Principle is related. Here a coil is moved in a magnetic field.
This induces voltages and current in the coil.