Notes in a melody are often described by the intervals between them, using a movement-based metaphor. An interval can be a "step" (neighboring notes in a scale--which are sometimes considered to be steps on a ladder) or a "leap," when the interval is larger than a single step.
Continuing with the movement metaphor, if the leap is downward in pitch, it is called a "falling" interval. If it is upward in pitch, it is a "rising interval".
Sometimes it is fair game to take this further if the melody has particular or striking movement characteristics, e.g., a gentle rocking motion, like a lullaby, or a more jagged or thrusting shape (think "Ride of the Valkyries") or a more circuitous or wandering shape (e.g., the pastoral English Horn solo in William Tell Overture), or 'sighing' like the first melody in Schubert's 'Unfinished'.
As you get more technical, harmonic characteristics (scale, chord) and rhythmic characteristics (strong beats/weak beats, passing tones, syncopation) as well as motif, phrase and sentence structure are discussed.