One could argue it can engage or move the listener. Or it could bore the listener. Or it leads one through the piece or various other airy fairy but still correct answers.
I'm guessing you're after some technical answer here? According to Wikipedia,
http://en.wikipedia.org/wiki/Melody
"The essential elements of any melody are duration, pitch, and quality [timbre, texture, and loudness]." (DeLone et. al. (Eds.) (1975). Aspects of Twentieth-Century Music, chap. 4, p.270-301. Englewood Cliffs, New Jersey: Prentice-Hall.)