horizontal vs. vertical
If by horizontal, you are referring to the movement of pitches plotted against time, as in music notation, the melody is indeed a "horizontal" construct composed of a series of single notes. If you think about the chord structure, it is the "vertical" component of this construct, with the melody (at least for the most part with some exceptions), usually incorporated into the pitches that make up the "stacks" of chords.
Usually, the melody is made to "stand out" against the backing chord structure, much as the main subject is made to stand out against the background in a painting or photo, or the main character in a novel or play against the setting and other characters.
In instrumental music, there is sometimes more "blurring" of the melody line vs. the chord structure. This would be evidenced by an inability to "hum the tune" of the song. This is a matter of style, similar to a painting or photo in which the subject is not readily separable from the whole of the composition.
Matt
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