The displacement, along the direction of measurement, is zero.
It need not mean that the object is back at the starting point. The displacement-time graph, measuring the vertical displacement of a ball thrown at an angle, will have displacement = 0 when the ball returns to ground level but, unless you are extremely feeble, the ball will be some distance away, not at its starting point which is where you are.
The use of such a graph is not unusual in the elementary projectile motion under gravity.
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Displacement is the area under the v-t graph.
It is the instantaneous speed in the direction in which the displacement is measured.
As, in the velocity-time graph, curves passes through zero means 'when time is zero velocity is zero'. Velocity is time derivative of displacement. So displacement is maximum or minimum when time is zero in position-time graph.
It is time.
Of course yes. An object is stationary when the graph is horizontal in a displacement-time graph.