Allusion is one of the lesser known figures of speech. This is how Merriam-Webster defines allusion:
“..a figure of speech, where a direct reference to a particular object, person, event or situation is supplanted by a muted and indirect reference to the object or incident.  The listener or reader has to make the connection. For example:
“He alluded to his parent’s bitter divorce’ means he did not talk about it directly but he may have said something like ‘That awful summer in 2001’ (the year his parent were divorced).”
“She alluded to the incident long ago, but she did not actually mention it.”

Synonyms for allusion:  reference to, mention of, suggestion of, hint about, an intimation of, comment on, remark on.

Umberto Eco, famous writer, made this memorable remark about allusions in written and spoken English:
“Never affirm, always allude: allusions are made to test the spirit and probe the heart.” 

Allusions are very common in biblical and religious texts, in songs, in literature and even in advertising.   Allusion is an indirect reference to a significant personal (good or bad), or political, historical, scandalous, notorious event. when you allude to something it means you do not name it directly, and you do not discuss it in detail.  It is really a passing comment, a brief aside that the listener or reader must be quick and informed enough to pick up on because that is all he will get on the subject. There are many examples where an allusion is used as literary device.  Allusions are quite common in everyday language and speech.

examples of allusion

“He was a Good Samaritan yesterday when he helped the lady start her car.” This refers to the Good Samaritan story in the Bible.
“He is her Romeo.” This refers to the powerful love between Shakespearean characters, Romeo and Juliet.
“Chocolate is her Achilles heel.”  Compares a woman’s love of chocolate to the story of the vulnerability of Achilles’ heel to Paris’ arrow.
A more contemporary example of allusion can be found in the song lyrics from Hey Juliet by boyband, LMNT:
I think you’re fine
You really blow my mind
Maybe someday (someday), you and me can run away
I just want you to know
I wanna be your Romeo
Hey Juliet
(Hey Juliet)
(Hey Juliet)

The beauty of allusion is that it “enables writers or poets to simplify complex ideas and emotions.” states the webpage www.literarydevices.com.  Allusion is an indirect reference to a significant personal (good or bad), or political, historical, scandalous, notorious event. When you allude to something it means you do not name it directly, and you do not discuss it in detail.