A few excerpts from the wonderful work (Lataa'if al Maa'rif) of Al Hafith ibn Rajab رحمه الله.
** Fasting the six days
of Shawwal completes the reward for fasting a full year.
** Fasting these six
days and previously fasting in the month of Shabaan (prior to Ramadhan) is
similar to the sunan ar-rawaatib (voluntary prayers associated to each
obligatory prayer). These prayers proceed and succeed the obligatory prayers,
and correct the deficiency and insufficiency present within them. Indeed
voluntary prayers strengthen and perfect any deficiency present within
obligatory prayers as has been mentioned by the Messenger صلّى
اللَّهُ عليه وسلّم
in several narrations. Most people possess fault and defect in their obligatory
prayers, and because of this the Messenger صلّى اللَّهُ عليه وسلّم forbade
a person from saying: I have fasted and stood (in prayer) the full month of Ramadhan.
(Abu Dawud, Nisa'ee) A companion upon hearing this hadith said: I don't know if this forbiddance was due to dislike of
praise or due to defect present in the act of worship.