Bhai Phonta, or Bhratri Dwitiya, falls on the second day of the bright fortnight of Kartik, two days after Kali Puja. Sisters put a phonta, a mark, on their brothers' foreheads and pray for their long life; the day is also called Yama Dwitiya.
By the old story, on this day Yamuna fed her brother Yama and marked his forehead; hence the rhyme's line about a thorn at Yama's door.