The importance of an allusion is what the word used represents. Allusion is used to refer to a person, place, event, or thing without naming it directly. It is up to the reader to then make the connection between the word used and the meaning implied. Allusion allows the reader to open their minds and interpretations of a story to a greater extent that what is written on the page. An example of allusion would be calling someone a "Romeo" - using the name implies a connection to the play Romeo and Juliet, and carries with it the characteristics of that character being applied to the subject of your comment.