In Rabindranath Tagore's "The Postmaster", the narrator details a line in which the Postmaster tells Ratan to leave the fire be and to come in and light his pipe. It is in this line where the phrase "with puffed out cheeks" appears.
The reference to "puffed out cheeks" refers to the holding of Ratan's breath to blow onto a coal so as to keep it burning so that he can light the Postmaster's pipe. Blowing upon a coal causes the coal to stay burning after taken from a coal pit or fire place.
Simply, "puffed out cheeks" refers to the pyhsical protrudence of Ratan's cheeks so that he may hold in enough air to keep the coal lit so that it does not extinguish before he is able to light the pipe of the Postmaster.