The story "Rikki-Tikki-Tavi" contains the word "veranda" a total of eight times. The usage of the word is not special or unique in the story, though. Kipling uses the word according to a standard dictionary definition of veranda: a roofed platform along the outside of a house, level with the ground floor (see my second link below).
That definition contains some specifics that are unique to verandas. First, a veranda is roofed. It's open to the elements from the front and/or sides, but it is covered. A person could sit in the veranda and would not get rained on. That makes it different from an open deck that some houses might have. Second, a veranda is level with the ground floor. If it was even with any other floor, it would be called a balcony or deck. The point of a veranda is to extend the living space of the house. It's not meant to be used as a bedroom, but it could be used as a living room or dining area. That is how the family in "Rikki-Tikki-Tavi" uses the veranda.
Early in the morning Rikki-tikki came to early breakfast in the veranda riding on Teddy's shoulder, and they gave him banana and some boiled egg.