Pronunciation: ar pedge ee oh
The word comes from Italian.
L'arpa - the harp
arpeggiare - to play harp
arpeggio - playing of the harp
I had always found the best way to learn is to totally relax it and play the sixth string with the thumb, relax the hand completely, then play the third string with the index finger, then relax completely again. Really stop playing and relax completely.... After that, you play the the second string with the middle finger, after which a complete stop with total relaxation follows, then play the first string with the ring finger, stopping again with total relaxation. Go back to the middle finger on the second string, then the index finger, ending again with the thumb on the sixth string as you had begun.
Do this exercise REALLY slowly allowing time to stop inbetween the notes for a total relaxation. By doing this, you are training the fingers where to go. After doing this for like 20 minutes or so, you should be playing this arpeggio, after which it is only a matter of learning different combinations of the same thing. Hope you understood all that. It should help you further.