The standing wave is also known as a stationary wave which continues to oscillate but t he profile of the peak amplitude does not moves with respect to space. At any point in space the peak amplitude remains constant with time and the oscillations of different points remain in phase throughout the wave.
The phenomenon of standing wave can occur either when the medium moves opposite to the direction of the wave or in a stationary medium a standing wave can form due to the interference of two waves that are moving in opposite direction.