This article in French shows that fasting the six days after Ramadan is an evidence on the fasting person's thanks to his Lord almighty for His easiness of fasting Ramadan, increase in goodness. It is also a sign of loving the righteous deeds and a desire to continue in this righteous path.
In this grate season of fasting, Muslims obey the commands of Allah (SWA) and the Sunnah of the Prophet Muhammad (PBUH). This is the month of Quran, mercy, happiness, and peace.