William Shakespeare has quite a legacy. If you really think about it, he is probably one of the most well-known, enduring authors of all time. He wrote plays and poetry that are, hands-down, the most discussed, debated, taught, read, analyzed, criticized, enacted, dramatized, spoofed, and quoted pieces of literature that exist today. From junior high to a doctorate's level, students study Shakespeare. It is nearly impossible to not encounter something that has been influenced by Shakespeare's writing, even if it's as little as a quote ("To be or not to be, that is the question" is used ALL the time, even in commercials--"To eat a taco, or to not eat a taco, that is the question"), or as immersed as an entire course that extensively studies his plays.
Take all of that information, the sheer breadth and impact of his work, and connect it to the fact that he wrote his work over 400 years ago, in English that has greatly evolved since then, in language that is incredibly difficult to understand, and with cultural quirks and innuendo that are long since history. That makes it even more amazing that his plays are still read. Having to struggle through English from 400 years ago, that is set in a place that is long distant, with scenarios that are often very specific to that culture, is not an easy task. Yet people do it all of the time.
Why does his work endure? Because Shakespeare had a talented understanding of human nature. He delved deep into the human psyche, and wrote plays that touch on themes that will be forever relevant, moving, and inspiring: Death, love, jealousy, hatred, insecurity, madness, self-esteem, passion, revenge. His themes and characters are so well-rounded and developed that once you understand them, it is impossible to not feel a personal connection. That is what makes Shakespeare relevant, universally appealing, and enduring. Yes, he is an immortal figure in literature, because his works have already lived beyond him, and will continue to perpetuate his legacy across the generations. I hope that those thoughts helped; good luck!