What do flat sections represent in a distance-time graph?

Object is at rest, stopped, not moving.

No movement. A break in journey.

Flat sections show that the object is stationary. For these sections, the distance doesn't change over time - the object doesn't accelerate or decelerate, or continue at a steady gradient. It has stopped.

On a distance-time graph, when the line is horizontal it means that the object is not moving.