When a melody or segment of music moves mostly in step-wise fashion using notes of the underlying scale. (Read Scales, Keys, and Key Signatures for a tutorial on what a scale is and how the different types are created). A scalar melody uses both chord and non-chord tones, compared to an arpeggio which uses only chord tones.
Scalar melodies are not restricted to continuous movement in one direction. “Scalar” simply means that consecutive notes mostly move a scale step up or down. There can be some interval leaps beyond scale steps at times. The predominant movement is step-wise, ie. scalar, but not exclusively so.
Scalar melodies are somewhat dissonant because they use notes that do not occur in the underlying harmony. These non-chord tones clash with the harmony, anywhere from mildly to startlingly so. Scalar and arpeggiated melodies have distinctly different sound qualities. Composers blend the two together to create melodies of vastly different and varying character.
Section B in Di Sarli’s Bahia Blanca begins with an unaccompanied bandoneon melody playing a short arpeggio, just the first four notes, then the melody descends down a scale in the second bar. Notice the character difference between the arpeggio and the scale:
Bahia Blanca, Section B, the first 4 Bar Phrase, bars 17-20.