The lunar month in which the sun does not transmigrate clearly is called adhik mas- additional month. It is also termed a residual month. The Jyotish texts mention how this naming came about:

Shakunyadichatushkam tu ravermalamudahrutam,
tadurdhwam kramate bhanormasaha syattu malimluchaha

i.e. the four Karanas, namely Shakuni, Chatushpad, Nag and Kimstugna are the sun's residue. The duration of transmigration that occurs in these Karanas is called the residual month.

In Jyotish's Falsamhita, great merit is attached to the Karana in which the sun transmigrates. That is, out of the 7 Karanas beginning with Bav, etc., the 4 Karanas namely Shakuni, etc. (cited above) are rather stable and are termed the residue of the sun. Therefore the transmigration that occurs in these 4 karanas is known as the residual month. This occurs once every 32 months.

Ban on performing auspicious rituals in the Residual Month
The ancient sages declared that when the moon is in the sun's aura (mandal), and if at this time, the sun transmigrates from one zodiac (sign) to another, it destroys the merit of the yagna, or other rituals. Therefore auspicious rituals should not be performed during this period. Instead holy acts and deeds such as bathing (in sacred rivers), donation, listening to kathas, etc., for propitiating God, should be performed, rather than idling away time.

Origin
There are several stories associated with Purushottam Mas.

1. In ancient times, the rishis Asit, Deval, Angira, Vamdev and others gathered at Naimisharanya Kshetra. Soon Sutpurani too arrived, while on a pilgrimage. Welcoming him, the others requested him to do katha which would imbue moksha.

   Sutji replied, "Once Naradji visited Nar-Narayan rishi's ashram. He humbly prayed, "O Prabhu! What is the way to moksha in this KaliYuga - age of darkness, which is plunging in ever increasing hedonism?"

   The rishi replied, "O Muni! If man was to listen to the divine lila of Purushottam Narayan, then even in Kali Yuga, He will grant moksha."

   Therefore the rishis listened to the lila in Adhik Mas, henceforth also known as Purushottam Mas.

2. Prior to this name, the month was known as Mal Mas (meaning waste).

   Since the sun did not enter any rashis during Adhik Mas, people considered it inauspicious and hence referred to it as waste.

   Grieved by this blot, Adhik Mas took the form of a human and travelled to Vishnu in Vaikunth. With heartfelt prayers he requested to be delivered from this ignominy and attain honor. Merciful Vishnu blessed him, gracing him Shri Krishna's darshan in Golok.

   In turn Shri Krishna blessed him with the boon, "Henceforth I have accepted Mal Mas! From today, I will uplift him to a status similar to mine."
   
   Atanmasadhipashchaham mayaivayam pratishthitaha,
   Purushottameti mannama tadapyasmai samarpitam.

   i.e. "All the virtues that have rendered me fame as Purushottam in this world, and my name Purushottam, I gift both to this month!"

   Shri Krishna then added, "Whoever performs satkarmas - good deeds in this month, their misery will be eradicated by these satkarmas. Those who perform penance in this month will conquer their indriyas - senses. Whereas by performing satkarmas in other months one attains Swarg, and also returns (to earth) after their depletion, performing them in Purushottam Mas will totally eradicate punarjanma - cycle of rebirth.

   He then added that, "I will forgive all the sins of those who perform penance in Purushottam Mas.

3.  Another story relates how Draupadi, in her past birth as Medhavati suffered spinsterhood. Durvasa rishi instructed her to perform penance in Purushottam Mas, which she hotly refused. Therefore she suffered Durvasa's curse. To be delivered from his curse she prayed to Mahadevji. When this pleased him, she blurted out a request for a husband five times! This resulted in her being married to the five Pandavas in her next birth, as Draupadi.

   Additionally, for insulting Purushottam Mas, she suffered humiliation at the hands of Duhshasan in a packed assembly.

   Later, after hearing Purushottam Mas's katha from Shri Krishna, the Pandavas and Draupadi performed penance in this month and attained peace.

4. Purushottam Mas's glory is such that performing penances in any form even unknowingly in this month imbues spiritual merit.

   Once a wealthy king named Dradhdhanva in his former birth, being childless, performed penance for a son. When the son was 12 years old he died. In great grief the king and queen forsook food and sleep for a month, sitting near their son's corpse. This month was Adhik Mas. This earned them Paramatma's grace, who then resurrected the boy!

• In this month, devotees awaken at Brahma Muhurt - around 4.30 a.m. After the ritual ablutions, they perform puja.
• They do pranayam for physical and mental purity. If circumstances are favorable devotees should offer Shodshopchar puja - worship with 16 different types of materials.
• If physically healthy, devotees should fast; either on water only for the whole month, or do farar, or ektana - one meal a day. The days should be devoted to listening to katha.
• The merit of this vrat is greater than that of performing a hundred yagnas, since this leads to attainment of Paramatma's abode.