The Messenger of Allah (Allah bless him and give him peace) said, “Fasting Ramadan and following it with six days from Shawwal is like continual fasting.” (Sahih Muslim)
This is because the reward of actions is multiplied (at least) ten-fold. So Ramadan is like fasting 300 days, and the six days of Shawwal like fasting 60 days. The Prophet (Allah bless him and give him peace) himself stated this explicitly: “Fasting Ramadan is like fasting ten months, and fasting six days [of Shawwal] is like fasting two months. That is like fasting a full year.” (Sunan Nasa’i)
Why is there so much reward and specifically why was Shawwal mentioned? Islam’s axis is submission. The meaning of Islam is to attain peace from Allah by submitting oneself. After enduring 29/30 days of fasting 16-18 hours a day, fasting for an additional 6 days truly displays your submission and loyalty to Allah the Almighty. It is a test of one’s chivalry and faith. It is a criterion to distinguish between the close and the closest. Only those immersed in sincere love for Allah can live up to the test.
The relationship between the 6 fasts and the fast of Ramadhan is akin to the relationship of the obligatory salaah and the voluntary (nafl) salaah; one complements and put the finishing touches to the other. The supererogatory prayers fill the holes remaining from the mandatory. Likewise, the 6 fasts of Shawwal wire up any loose ends remaining from the fasts of Ramadhan.
There are many actions which effectively patch up deficiencies. In Umrah, two rakaats must be offered after circling (tawaaf) the Ka’bah. After the sa’y, it is recommended to perform two additional rakaats. Many ahaadith encourage volunatary monetary advancements. The prophet (Allah bless him and give him peace) commanded the traders to render a voluntary payment upon the closing hours of business. The Prophet would recite Istighfaar in abundance upon the termination of a meeting or gathering. All these acts and many more of the like bridge the gap between complete and incomplete.
In addition, these fasts are there to take the place of the prohibited days to fast: the two days of ‘Eid and the three days of tashreeq. (Awjaz al-masalik 4/358)
Majority of the leading scholars; Imam Abu Hanifah, Imam Shafi’i and Imam Ahmed recommended the six fasts of Shawwal. (al-mughni 4/438)
However, Imam Malik’s stance was different on this issue. He disliked the laymen fasting these days in fear that they would regard it to be at par with the fasts of Ramadhan. (Mawaahib al-Jaleel 3/329)
The Shafi’i school recommend one to fast the six days consecutively. The deduced this ruling from a hadith reported by Tabarani in which the Prophet (Allah bless him and give him peace) said, “Fasting six days consecutively after ‘Eid al-fitr is like fasting the entire year.” Whereas scholars of the Hanafi and Hanbali schools have left the sequence of fasting at the discretion of the individual; it will be permissible to fast consecutively as well as inconsecutively. The Hanafi and Hanbali scholars categorised the hadith mention by Tabrani as weak. In addition to this, they mention that the hadith reported in Sahih Muslim is absolute (mutlaq); it is free of any restrictive words. Hence, it can be deduced from here that any six days of shawwaal will suffice for one to acquire this reward. (mughni al-muhtaaj 1/654) (Radd al-muhtaar 3/422) (al-mughni 4/438)
The best course of action would be to fast consecutively, thus creating harmony between the varying opinions.
If somebody fasts six fasts in Shawwal as make-up (qadha) or vow (nazr), it is hoped from the mercy of Allah that one will still attain the reward of fasting six days in Shawwal. It would be better to perform the make-up (qadha) fasts exclusively and perform the six fasts with an exclusive intention. (mughni al-muhtaaj 1/654)
This answer was collected from DarulFiqh.com, which is operated under the supervision of Mufti Faraz ibn Adam al-Mahmudi, the student of world renowned Mufti Ebrahim Desai (Hafizahullah).