A waterfall of notes will tumble from your guitar as your left hand holds down a chord shape. Your right hand is parked over the strings and your right wrist is still. But the fingers of your right hand are spooling out patterns called "arpeggios" or "broken chords."
Arpeggios are one of the great assets of the guitar and twin pillars of technique in all instruments and voices, along with Scales: The right hand thumb (p), index (i), middle (m) and ring (a) fingers can break up a left hand chord into patterns. Here are the top ten patterns you need to know for classical guitar repertoire: pim, pmi, pimi, pimipi, pia, pai, piai, pima, pami, and pimami.
I'd like to quote a guitar hero of mine, Pepe Romeo, on a particular set of arpeggio exercises from another great guitarist from an earlier era - the Italian virtuoso and composer Mauro Giuliani:
"It is with the deepest respect and admiration for one of the greatest masters the guitar has ever had, Mauro Giuliani, that I present his 120 daily right hand studies. Not only has this great genius left us with an incredible wealth of music, but he has also left us the 'formulas' by which to play them. To this day I hold them as an indispensable part of my training."
To get your copy of the 120 Daily Studies for the Right Hand, by Mauro Giuliani, call a store like Music Music Music or Guitar Solo and have them sent right over. Play them slowly and enjoy the lessons as they unfold. I recommend planting all ascending arpeggios, and be sure not to play faster than you can play well. Your speed will increase sooner if you keep your hand generally relaxed. That's right - you can have a relaxed hand while fingers are moving in sequence, just as a piston in an engine fires and then waits to fire again. The key is to empty the tension of a movement as soon as it happens.
Here's an exercise to demonstrate this dea. Click your finger in your right hand once a second several times. Each time you reset to click again, you're in a relaxed and ready mode. That's what happens for each finger in arpeggios when you play with a relaxed technique. If you let excess tension creep in to your playing, it will definitely limit your speed.