An arpeggio is a chord played one note at a time. The following example demonstrates a C chord played first as a chord (strummed) and then as an arpeggio (picked). Playing chords as arpeggios is a common way of creating guitar parts in a band situation.
Here is an example which makes use of arpeggios. Hold down the chord shapes indicated as much as possible except when playing notes which are not in the chords (e.g. the B note at the end of bar 2). Take care with your picking and make sure all your notes are clear and even.