An arpeggio is a chord played one note at a time. The value of arpeggios is that they enable you to play lines which fit chord progressions perfectly, since every note of an arpeggio is a note of the accompanying chord. Written below is a C major arpeggio which consists of the notes C, E and G. These are the root, third and fifth of a C major chord.
Here is an F major arpeggio which consists of the notes F, A and C. These are the root, third and fifth of an F major chord.