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

The object is travelling at a constant velocity, (usually) at a constant speed.

When the line is horizontal in a velocity-time graph this means that the speed is constant (not changing).

The velocity of the object is constant. This means that it is travelling in an unchanging fixed direction at the same speed throughout.

A flat section in a velocity-time graph represents a time period in which velocity is constant (i.e. not changing in value).

It represents an object travelling at constant velocity

The flat sections on a velocity-time graph show that the object is moving at a constant velocity, or in other words, it is not accelerating.