Good question! By definition, an allusion is a passing reference-- in a work of literature-- to a person, place, character, historical event, biblical passage, other work of literature, work of art art, or piece of music that the author expects readers to recognize and understand. Authors include allusions in their works to help readers get a better understanding of the situation that's being discussed or described in the text.
In "The Most Dangerous Game," Richard Connell makes use of this literary device quite frequently.
On the first page of the story, Whitney says, "I hope the jaguar guns have come from Purdey's." As Purdey's is a famous manufacturer of shotguns and rifles, Connell includes it in the story so readers familiar with the brand will understand that Whitney and Rainsford are avid hunters.
Further, General Zaroff labels Ivan as a "Cossack," which is a term to describe a person from the southern part of Russia; Cossacks were known for their impressive battle-skills. Thus, Zaroff establishes Ivan as a fierce hunter whom Rainsford should be afraid of.
Also, as Rainsford rushes around in the forest trying to devise a plan to elude General Zaroff, Zaroff sits in his home, drinking and smoking a cigarette, and humming a tune from Madame Butterfly--a famous opera by Puccini. Then, before bed, he reads "from the works of Marcus Aurelius"--a Roman emperor.
Connell makes these references to help readers understand his story and the characters/situations in it.
Hope this helps!