Arpeggios are a great way to establish thumb and finger independence because all your digits are required to execute them well.
Basically an arpeggio is a chord played one note after the other. You can play arpeggios with a forward roll (ascending) or a backwards roll (descending), or a combination of forwards and backwards. But whichever way it goes the arpeggio should sound nice and smooth. Eradicate jerks and aim for even volume and tone for each note.
Hopefully you can see why you need to use your thumb (p), index finger (i), middle finger (m) and ring finger (a). Some players dispense with the ring finger but this means that their middle finger has to play a string and then drop down to the next one which is fine if the tempo is slow, but when things speed up it