A biblical allusion is a very quick or indirect reference to something in the Bible, such as a particular scripture, character or story. Examples could include comparing a modern place to somewhere in the Bible, like the Garden of Eden or Sodom and Gomorrah, or comparing a person to the Good Samaritan.
The word "allusion" can be thought of as a fancy term for "reference." When authors or other people make an allusion, they are referencing another well-known story, time period or person. For an allusion to work properly, the other person must possess a thorough knowledge of the subject of the allusion.