The answer to your question would be that the euphemism in the sentence politely masks any unpleasant details of the mayor's illness.
Explanation:
The term "euphemism" refers to polite, indirect expressions that replace words and phrases considered harsh and polite, or which suggest something unpleasant. The fact is that it is not necessary to know the details of the mayor's illness if he/she is not dealing with a severe disease. Therefore, the euphemism avoids the inclusion of any detail.
