Jazz is certainly a genre that lends itself to much musical expression because of the improvisation that enters into the playing of jazz. The jazz player must inherently have a good "ear" for his/her music and then can insert "licks" into a piece or improvise in other ways, such as changing the tempo.
In a 1988 interview, trombonist J.J. Johnson said, "Jazz is restless. It won't stay put and it never will."
Some other unique characteristics of jazz that provide an interesting presentation of melody are the flatted fifth chords and modern harmonies and substitutions.
Sometimes musicians play their instruments in usual ways that create different sounds. For instance, there is a jazz violinist who sometimes turns his violin backwards and runs his bow across the neck. Trumpeters often place their hands or a mute inside the end of their instrument.
Another element of musical expression that creates interest is the mixing of genres. One popular mixture is what is called jazz-fusion, jazz that is combined with another genre. Or jazz with an ethnic tinge, such as jazz with a Spanish tinge gives a different expression.
There are as many answers to this question as there are situations in which music may be used to contribute to the overall reaction.
Consider the soundtracks of movies you have seen. Action films have soundtracks filled with emphatic rhythms, strong harmonizations using the full range of instrumental sounds, and tempos that reflect the rapid movements of characters through the plot. Science fiction films employ unusual combinations of instrumentation, minor keys or completely dissonant sounds with no set rhythmic pattern. Films set in actual historic periods feature music taken from or representative of the eras being recreated, which may involve combinations of instruments or developments of musical themes that are no longer commonly used.
Any of these elements, however, contribute to the impact of the music and support the overall impact of the movie upon the viewers.