In this absurdist and Kafkaesque story, Kovalyov wakes up one morning with no nose, just a flat spot where his nose was. This being very concerning to him, he tries to place an advertisement to locate the missing nose. While the man working in the newspaper printing office finally listens to what Kovalyov is talking about, he doesn't fully grasp it, and he refuses to run the ad on the grounds that it is inappropriate and potentially libelous. The employee then offers Kovalyov some snuff, a concoction of crushed tobacco leaves that are inhaled up the nose to give a person a nicotine hit. This is obviously a ridiculous offer, as Kovalyov has no nose.
The incident is significant because it shows the underlying truth of how difficult it can be for a person, especially in an official capacity, to understand or cope with an "out of the box" request. The newspaper employer simply can't empathize or offer help to Kovalyov, because Kovalyov's situation is too far outside of his normal context.
Kovalyov runs up against this problem repeatedly. It seems this problem would be easy to understand, if unusual, because people can look and see visual evidence of the missing nose. Nevertheless, even with the evidence in front of them, people in the story are, on the whole, unable to grasp the implications when something strange occurs.