An arpeggio is a chord played one note at a time. Learning arpeggios enables you to play melodies which fit chord progressions perfectly, since every note of an arpeggio is a note of the accompanying chord. Here 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.
Arpeggios are easy to play. You simply hold down the chord shape and pick the notes individually with your right hand fingers.
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.