Let's define what a uniformly accelerated motion in horizontal dimension means.
Uniformly accelerated motion can be said to be a motion whereby the body/object in motion is undergoing uniform acceleration.
If an object is uniformly accelerated it is moving at a constant acceleration.
When a body is uniformly accelerated, it is has a constant acceleration irrespective of time
In this case, when there is uniformly accelerated motion in the horizontal direction, it means the object in motion is undergoing uniform acceleration and moving along the x-axis(horizontal axis).
Therefore, a uniformly accelerated motion in the horizontal dimension means that an object/body in motion is undergoing uniform acceleration and is moving along the x-axis.
ANSWER:
A uniformly accelerated motion in the horizontal dimension means that an object/body in motion is undergoing uniform acceleration and is moving along the x-axis.