An allusion is a casual or indirect reference to something of cultural, literary, political, or historical significance. They can sometimes be difficult to spot, because authors will often choose allusions to things in popular culture, which of course changes with time and location.
Book eleven of the Odyssey is full of allusions, which can be found in the list of the dead Odysseus encounters. When he says, "I also saw fair Epicaste mother of king Oedipus," that is an allusion to the story Oedipus Rex, in which Oedipus unwittingly kills his father and marries his own mother. He also sees "Eriphyle, who sold her own husband's life for gold," which is an allusion to Amphiaraus, who died in a war after his wife, Eriphyle, convinced him to go fight after Polynices bribed her with the necklace of Harmonia.
I don't know if you have to write your own original allusion or simply come up with an example not from the Odyssey. If it is the latter, saying someone will open up "Pandora's box" is an allusion to the myth of Pandora, who opened up a container that released all the evil into the world. Any time someone talks about the "garden of eden" or "forbidden fruit" they are alluding to the Biblical story of Adam and Eve. There are plenty of allusions that have become so common in every day speech that people don't even think of them as being allusions anymore. Perhaps you are supposed to make a modern allusion, in which case even something as simple as describing a teacher as a "total Snape" is an allusion. Anyone familiar with the Harry Potter series would know that teacher is not a nice guy. If you need to make up your own, just remember that it needs to be significant in some way. Other than that, you are limited only by your knowledge of other works, historical figures, and so on.