What makes a work of literature a “classic”?

A work of literature is considered "a classic" if it has lasted through the proverbial test of time; that is, if it has an appeal that is enduring and it speaks in a universal manner to the human condition.
Enduring appeal
Despite the time period in which it is written, a classic work of literature remains appealing because it delights and interests readers on several levels. For example, Mark Twain's The Adventures of Huckleberry Finn—certainly a classic—holds the interest of young readers who delight in the various escapades in which Huck is involved, such as the defeat of his cruel Pa and others who attempt to harm him and Jim, as well as Huck's maturation. Similarly, adult readers delight in Huck and Jim's escapades for their humor, but they are also able to enjoy the satire of society in Twain's writing.
Universality
Classics speak to the human condition; that is, there are themes and characterization in classic literature that address the basic aspects of birth, growth, hopes, feelings, conflict, and mortality in human life. These matters addressed are universal and do not just pertain to a certain country or race. This is why a Korean girl, for instance, can read Great Expectations and enjoy it as much as an American boy. They can both relate to Pip, who wishes to better himself since being treated unfairly because he is "coarse and common."