This exercise is taken from one of the Classical Guitar masters, Matteo Carcassi.  Carcassi wrote an Opus 60 with 25 Etudes in them.  Each Etude combines a classical technique mixed with a classical music idea.  If you take the time and work through all 25 Etudes you will be well on your way to mastering fingerpicking on the guitar.  This exercise is taken from his 2nd Etude and combines a basic arpeggio followed by 4 plucks of the same note on the same string.  Many fingerpickers only ever do variations on arpeggios.  This exercise is designed to get you used to finger picking the same string multiple 

Practicing Tips

This 4 measure exercise is taken from the first 4 bars of Carcassi's 2nd Etude.  The chord progression switches between A minor and E several times.  The chording is limited to the top 3 strings of the guitar making the fret hand chords fairly easy to play and transition between once you are familiar with the chords.  Each chord stays static and doesn't change for the 2 beats it is played.  Since there is no movement within each chord, the fret hand is pretty straight forward.