There are two basic sources for calendars in the world namely Lunar Calendar and Solar Calendar. First let us know what Lunar and Solar Calendars are. A lunar calendar (Chandramana) is a calendar that is based on transit of Moon into the each Nakshatra (star) starting from Ashwini (Beta Arietis) to Revathi (Zeta Piscum). While Solar calendar (Souramana) is a calendar that is based on transit of Sun into the each Rashi (Zodiac) starting from Mesha (Aries) to Mina (Pisces).
Ancient seers found that Sun remains in a zodiac sign for approximately one month, the Moon travels through all twelve zodiac signs in about Twenty Seven and half days. As a result, on average, once about every two and half years, the entry of the Moon in the same zodiac sign occurs twice while the Sun remains in the same sign. In other words, when the Sun is traveling through the same zodiac sign, the month during which two new moons occur, happens once about every two and half years. This would result in sliding of a lunar month in relation to solar year. Such progressive slump of lunar months leads to disparity in seasons which depend on solar calendar. In order to synchronize the lunar months with solar calendar and to keep in pace with the seasons ancient seers formulated a concept or technique of adding an intercalary month for the lunar calendar.
Even this happens in Gregorian calendar also normally a month has only one new moon (Amavasya) and one full moon (Pournami). Sometime in a month two new moons occurred (it is very rare and called Blumoon). We can see that there are two full moons this month August 1st we had one and coming 31st there is another. In the same lines once in a while may be in 3 years, there will be no transit of Sun to any zodiac between two new moons such a month is termed Adhika Masa.
When was it suitable to add an extra month????
Adhika Masa, an extra month in the Hindu Lunar Calendar is also called Mala Masa. Adhika Masa happens to be from August 18 to September 16. Intercalation is the insertion of a leap day, week or month into some calendar years to make the calendar follow the seasons or moon phase. If there is Sun’s transit between two new moons (Amavasya) then it is a normal month, if there no Sun’s transit between new moons, it is considered Adhika Masa which happened this time. Sun transit to Simha Rashi (Leo) took place on August 17th and stays in that zodiac till September 16th there is no new moon (Amavasya) between those dates hence this entire Badrapada Masa is Adhika Badrapada Masa. According to lunar calendar from September 16th onwards it is Nija Badrapada, while to solar calendar from September 16th onwards it is Kanya (Virgo) Masa.