Arpeggios are just the notes of a chord played individually from lowest to highest and back again to the tonic. For example the notes in a C6 chord are C E G and A , being the 1st 3rd 5th and 6th notes of the C major scale. By playing these chord tones separately we are playing the C6 arpeggio. Soloists use arpeggios when improvising to clearly outline the underlying chord changes in a song. By playing the chord tones over the top of the chord upon which the arpeggio is built the soloist creates a very INSIDE sound. The opposite to this would be to play those notes not in the chord, such as the extension notes , 9ths 11ths and 13ths , as well as passing tones to create an OUTSIDE sound.
Clearly, a solo that is too INSIDE, can become predictable, just as a solo that doesn't appear to relate to the chord changes will sound too OUTSIDE for most people to understand , with the theme and mood of the song becoming too abstract. Achieving the right balance, as in everything in life , is the key to creating an enjoyable, interesting and exciting solo. A combination of VERTICAL (moving up and down the chord tones) and HORIZONTAL (moving along the scale tones) playing style, will usually achieve a good result.
The examples of arpeggios below should be played as smoothly as possible, gradually building up speed as you become familiar with them. The arpeggio diagrams should be played from the Tonic (in Red) through the sequence of chord tones from lowest to highest , then back down in reverse order. E.g. if the arpeggio formula is 1 3 5 7 as in the C major7 chord, the notes to be played would be C E G B C B G E C , this is the correct sequence that they should be played.