Sri:
1. hemante prathame māsi nanda-vraja-kamārikāḥ
cerur haviṣyaḿ bhuñjānāḥ kātyāyany-arcana-vratam
2. āplutyāmbhasi kālindyā jalānte codite 'ruṇe kṛtvā pratikṛtiḿ
devīm ānarcur nṛpa saikatīm gandhair mālyaiḥ surabhibhir balibhir
dhūpa-dīpakaiḥ uccāvacaiś copahāraiḥ pravāla-phala-taṇḍulaiḥ
3. kātyāyani mahā-māye mahā-yoginy adhīśvari nanda-gopa-sutaḿ devi
patiḿ me kuru te namaḥ iti mantraḿ japantyas tāḥ pūjāḿ cakruḥ kamārikāḥ
---Bagavata Purana 10.22.1 - 3
During the first month of winter season, the young gopis of gokulam, performed Kartyayini vrata. After they had taken the bath in Yamuna river, they made the deity of Goddess Karthiyayini with sandalwood paste and then started worshipping her with flowers, fruits, leafs and nuts. Then they started praying Karthiyayini with the mantra “Oh Goddess Karthiyayini, I offer my obeisances unto you. Please make Nanda-gopa-sutam (Krishna) as my husband”
These versus were composed by Sri Vyasa Bhagavan, and preached by his son Sri Suka to Parikshit maharaja.
The Kramam (order) of the slokas is notable here. It is what, how and why. Vyasa Bhagavan, in the first sloka explained what gopis did , second how, third why.
In Bhagavad Gita 9.26, Bhagavan says,
“Whoever offers me a leaf, flower, water with devotion , I accept all those offering from that pure hearted person“
In Thirupaavai andal says ,
Like wise, in many places our Acharyas say, Aayar kula gopis do not know even right hand and left hand. But Krishna Bhakti made them follow the vrata as per scripture injuctions. Lord needs only the Love to attain him, He does the rest fot us.
The time at which they observed Karthiyayini vrata is the first of of winter, “margazhi”. In Gita Bhagavan says “I am the month Margazhi”. In such auspicious month Gopis did the nonbu and got Krishna anubhavam.
Even Sri Mahalakshmi might not have received such anubhavam from Peruman, Sri Suka wonders in Bhagavatam.
The 6 years old Andal, who born to Periyaazhvar at thiruvilliputhur in Tamil Nadu , wanted that Bhagavad Anubhavam. When she was thinking of what to do to get such Bhagavad anubhavam, she came to know about the story of Gopis and Kartiyayini Vrata. Thus she decided to do the same and stated doing the vrata in Srivilliputhur. She herself became like gopi, with all their speech, walk, and all. Thus she got the Krisha anubhavam and such aubhavam came through her mouth as “Thirupaavai” with 30 pasurams.
-Adiyen.