Rudyard Kipling first tells readers that Rikki is curious, and then he gives multiple examples of the mongoose acting on his curiosity. The narrator states that it is very hard to frighten a mongoose because "he is eaten up from nose to tail with curiosity." This description is validated by the mongoose family motto, which is "Run and find out." Wanting to find out is another way of describing curiosity; adding a "run" to finding out intensifies the curiosity and qualifies it as an active, energetic curiosity rather than a mere intellectual curiosity.
The story then goes on to relate several things that Rikki investigate during his first day and evening in the bungalow: the cotton wool he had been wrapped in; the table; the inside of Teddy's shirt; the bathtubs; the ink bottle; the man's cigar; the kerosene lamps; Teddy's bed; and any sounds he hears during the night. The next day he proceeds to investigate the garden. He is curious about why Darzee is crying and about who Nag is. That night, he is curious about what Chua told Chuchundra, and then he ends up overhearing the conversation between Nag and Nagaina. His curiosity pays off because he learns of their plan to kill the man when he comes to bathe and he learns about their cobra eggs that are just about to hatch.
Because Rikki is "eaten up with curiosity," he is able to save the humans from being killed by the cobras and he is able to rid the garden of cobras forever.