An arpeggio is a chord which is played or sung one note at a time. As it is not possible to sing two notes simultaneously with one voice, singing an arpeggio is the only way a singer can sing a chord. The following example shows the arpeggios of C, F and G major which are the primary chords in the key of C.
It is also possible to sing arpeggios of any other type of chord, e.g., minor arpeggios, seventh arpeggios, diminished arpeggios, etc. Arpeggios are often used in song melodies. The reason they work so well is that they fit perfectly with any accompanying chord because both the melody and chords contain exactly the same notes.