"Kindly return my lawnmower" would be pretty aggressive in a note to a neighbour. As a result, inserting "kindly" into a request gives it the construction of a command. "Kindly keep your opinions to yourself" is an example of how it would be used to intensify a statement from brusque instruction to a threatening command tone. More @Wikipedia
Hover over any link to get a description of the article. Please note that search keywords are sometimes hidden within the full article and don't appear in the description or title.