When we apply the term "classic" to works other than those belonging to the ancient Greek or Roman periods, what we are saying is that the literary work belongs to a separate "class" of its very own.
This being said, when we read works often considered "classics", we find that their salient feature is that their main idea withstands the passage of time, changes in society, and the shifts in paradigms that occur from one era to another.
This is because it is often the case that the main themes of classic works are universal, but the narrator is conscientious enough to either catch, or re-create in detail, the sensibilities of the generation which the work represents.
In The Glass Menagerie Tennessee Williams uses a clever strategy where he picks the most typical (and perhaps even stereotypical) characters that can be found during a delicate time and place in history, such as it was the Great Depression, and the advent of WWII:
These characters are easy to relate to because their flaws and vulnerabilities transcend time and place: Tom is the lost tragic hero who is trapped between his conscious self, and his circumstances; his mother Amanda, a former Southern aristocrat is a direct victim of the economy and of a bad marriage; Tom's sister, Laura, is a crippled woman unable to catch up with a changing society; and the character of Jim represents a man once-expected to succeed, but his success has been hindered by the social and economic climate of the times.
This is a combination of personalities, issues, and human emotions; not just a combination of characters.
The fact that the plot takes place during a historical time in our society makes the work even more relevant to the reader. Yet, the connection that the audience can make from self-to-text is what solidifies the bond between the work and the reader. It is a synergistic dynamic where the reader feeds off the literature the same way in which the literature is possible thanks to its collection of genuine, human traits.