The "horizon" is the furthest you can see. "On the horizon" therfore refers to an object which is just in sight.
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You mean the horizon?
What it means is horizontal line is like the horizon it goes across
The distance to the horizon, d kilometres, is related to the height above mean sea level, h metres, by the approximate formula: d = 3.57*sqrt(h).
horizon 3 and horizon4
If you mean horizontal, it is left and right. I remember it as if you look at the horizon it goes from left to right, not up and down. Up and down is vertical. It is like the x axis. It is horizontal