-- A horizontal line on a position/time graph says that as time goes on, the position isn't changing. The object is standing still. At rest. Motionless.
-- A horizontal line on a speed/time graph says that as time goes on, the speed isn't changing. If that doesn't happen to be zero, then the object is moving at a constant speed, and its position keeps changing at constant rate. On a position/time graph, this same motion would be a straight line slanting upward.