“One of the most important of these ceremonial functions is called Urja-vrata. Urja-vrata is observed in the month of Karttika (October-November); especially in Vrndavana, there is a specific program for temple worship of the Lord in His Damodara form. “Damodara” refers to Krsna’s being bound with rope by His mother, Yasoda. It is said that just as Lord Damodara is very dear to His devotees, so the month known as Damodara or Karttika is also very dear to them.
“The execution of devotional service during Urja-vrata in the month of Karttika is especially recommended to be performed at Mathura. This system is still followed by many devotees. They go to Mathura or Vrndavana and stay there during the month of Karttika specifically to perform devotional services during this period. In the Padma Purana it is said, “The Lord may offer liberation or material happiness to a devotee, but after some devotional service has been executed, particularly in Mathura during the month of Karttika, the devotees want only to attain pure devotional service unto the Lord.” The purport is that the Lord does not award devotional service to ordinary persons who are not serious about it. But even such unserious persons who execute devotional service according to the regulative principles during the month of Karttika, and within the jurisdiction of Mathura in India, are very easily awarded the Lord’s personal service.” (Srila Prabhupada in NOD chap. 12)
durlabho bhakti-yogo me mama vasya-vidhayakah
karttike mathurayam ca vratenanena labhyate
“Pure devotional service to Me which, because it places Me under My devotee’s dominion, is very difficult to attain, is easily attained by following this vow in Mathura during Karttika.”
“To they who worship Krishna in Vrindavan, the Lord gives them their original spiritual forms. The perfect atonement to purify the sins of a lifetime is to worship Lord Damodara in Vrindavan during Kartik. The month of Kartik spent in Vrindavan brings the supreme destination.” -Srila Rupa Goswami, Mathura Mahatyam
“In the month of Kartik, which is very dear to Sri Hari, one who bathes early in the morning attains the merit of bathing in all places of pilgrimage. Anybody who offers the Lord a ghee lamp in the month of Kartik, O brahmana, becomes free from all kinds of sins, such as killing a brahmana, and he goes to the abode of Lord Hari.” (Brahma Khanda).
As Satya-yuga is the best of yugas, as the Vedas are the best of scriptures, as Ganga is the best of rivers, so Karttika is the best of months, the most dear to Lord Krsna - Skanda Purana
“Suta Goswami says, “If anyone fasts and observes the Kartik-vrata according to the rules and regulations, the Yamadutas, the messengers of Yamaraja, run away from him, just as an elephant runs away by seeing a lion. This dear fast [vrata] of Lord Vishnu is even better than performing one hundred great sacrifices that would take him to heaven because the person who observes the Kartik-vrata goes to the spiritual world.” (Padma Purana)
“Although one can easily reach Mathura [Vraja Mandala] on this earth, and although Kartik month is easily observable, and although in the month of Kartik all of the places of pilgrimage, oceans, rivers, and lakes come to the Mathura area, still, those human beings who are foolish and suffering in the ocean of material existence do not take advantage of it.” (Padma Purana)
Kartik is the best, the purest of purifiers, and most glorious of all months. Kartik month is particularly dear to Lord Sri Krsna. This month is full of bhakta vatsalya. Any vrata, even the smallest, will yield huge results. The effect of performing a Kartik Vrata lasts for one hundred lifetimes, whereas ordinary vratas only last for one lifetime! Srimati Radhika is the presiding deity of the holy month of Kartik. Rupa Goswami and others refer to Radharani as Kartik Devi; in other words, Radhika is the goddess or presiding Deity of the Kartik Vrata. - Padma Purana. : quoted by Srila Sanatana Goswami in his Hari-Bhakti Vilasa
Specifically in the month of Damodara, one should daily worship Lord Damodara and take bath early in the morning, give charity and follow a fasting vow. This is the duty of Vaisnavas. - (HARI BHAKTI VILASA 16/3 from SKANDA PURANA)
Oh son Narada, those brahmanas who do not give charity in the month of Karttika, perform sacrifice, chant japa and fast for Lord Hari are the lowest of mankind. - (HARI BHAKTI VILASA 16/25 from SKANDA PURANA)
There is no other month equal to Karttika and there is no other yuga equal to Krta-yuga. There is no other scripture equal to Vedas. There is no other place of pilgrimage equal to Ganges, therefore, the month of Karttika is very dear to the Vaisnavas (people dedicated to Visnu). - (HARI BHAKTI VILASA 16/39,40 from SKANDA PURANA)
Oh great sage, after giving up all varieties of religious functions, one should follow Karttika fast and listen to the narrations of Lord Sri Hari before His Deity form. - (HARI BHAKTI VILASA 16/76 from SKANDA PURANA Lord Brahma speaks to Narada Muni)
One rat (female mouse) had once burnt a ghee lamp which was offered by someone else on Ekadasi day. By doing so, she achieved a rarely achievable human form and at last attained the topmost destination. - (HARI BHAKTI VILASA 16/129 from SKANDA PURANA)