An allusion, according to the eNotes Guide to Literary Terms, is
a reference, usually brief, often casual, occasionally indirect, to a person, event, or condition thought to be familiar (but sometimes actually obscure or unknown) to the reader. This holds true especially for the characters and events of mythology, legends, and history. Association is an essential part of allusion. The purpose of allusion is to bring a world of experience outside the limitations of a statement to the reader.
An allusion is useful because it can convey a whole lot of meaning in a very short word or phrase, but it is not so essential that a reader or viewer must know the reference to follow the story. Knowing the original character, story, or event just enriches the experience for those who do.
For example, a reference to any kind of struggle as a David versus Goliath battle would be good news for the underdog (and bad news for the other guy) only to those who know the story. Those who do not know the Bible story would find out what that means, but they would lose the kind of anticipation which comes from knowing the outcome ahead of time but not knowing quite how it will happen.
A literary allusion to Atticus would be meaningless to someone who has never read To Kill a Mockingbird, but for those who have, what a wonderful compliment that would be. Conversely, if someone referred to a woman as "Grendel's mother," the picture would not be quite as flattering. And referring to someone as Zeus would be a mixed compliment, at best. References to great battles--either because of victory or defeat--are also meaningful if one knows the reference.
Because allusions are generally from literature, history, mythology, or the Bible, those who are most familiar with those things will be able to understand and appreciate them. Allusions give a depth and richness to things because they bring an entire storyline and characterization to something in just a word or two. In the case of a literary allusion, people also often have emotional connections which add another element to the work they are watching or reading.
Think of allusions as adding dimension to something flat or gradations of color to something which is monochrome--one dimension and one color are both fine, but both are better with the addition of dimension and gradation.