Why is the movie titled "Eternal Sunshine of the Spotless Mind"?

How happy is the blameless vestal’s lot!
The world forgetting, by the world forgot.
Eternal sunshine of the spotless mind!
Each pray’r accepted, and each wish resign’d
             ? Alexander Pope, Eloisa to Abelard

Charlie Kaufman, the sreenwriter of Eternal Sunshine of the Spotless Mind, is kind of obsessed with the dichotomy between embracing life unabashedly and keeping it at a skeptical and safe distance. He literally split his personality on the page for his script of Adaptation., where Nicholas Cage plays both Charlie (the skeptic) and Donald (the embracer.)

One of his key theses is to question whether it's possible to make genuine connections with other people, and to that end, one of his bugabears is the story of 12th century philosophy teacher Pierre Abelard and his charge Heloise.

The short version: Abelard taught Heloise and they fell in love. Heloise's family found out and had Abelard castrated. Abelard retreated to a monastery and convinced Heloise to move into an abbey. They then famously discussed the nature of their love in a series of letters.

Kaufman first references their story as Craig Schwarz's puppet show in Being John Malkovich. Craig's search for meaningfulness is echoed in their own writings, and like Abelard's penchant for selling his monastic lifestyle to Heloise as more spiritually and intellectually rewarding than their previous relationship, Craig feels more comfortable and happier living his "life of the mind" (in Craig's case, somewhat literally.) Abelard represents something akin to nihilism, a denial of pleasure, and a retreat within oneself.

Eternal Sunshine of the Spotless Mind expands on this idea in a different yet equally interesting way: by asking us to take stock of our memories and our pasts. In Eloise's letters, she mentions that in her dreams she still feels Abelard's touch and finds herself highly aroused by his presence there. She feels guilty about these dreams, and in Pope's poem she notes that only a life with no regrets can achieve happiness.

Pope's lines are powerful because they are (like the movie) a hopeless fantasy. The movie takes it one step further - even in its fantasy world where your memories apparently can successfully be erased, they still exist in others to haunt you; there's simply no escaping them. So in the film you have multiple people erasing genuine connections they did have; retreating into themselves; fighting those urges; and ultimately resigning themselves to a world that simply does not forget.

The film's title is a promise, and a wish, and a lie, all in one.

My interpretation is well represented by the term "ignorance is bliss". The point of the film is to create "spotless minds" by removing the memories that cause turmoil, jealousy etc. "Eternal sunshine" is a metaphor for ongoing peace, happiness and carefree. So in full "Eternal Sunshine of a Spotless Mind" is describing the happiness and joy one can experience once the negative experiences (or "spots") have been removed from your mind.

Wonderful answer, wonderfully stated. I would only add, that i think the film goes a little farther. Not only does memories being erased haunt you, it evokes the erasure of memory like an amputation...the "limb" is no longer there but you still feel the pain, and the ache of that loss. Quite literally, you become less human by this amputation, because our hearts and souls become deeper and more deeply enriched by the joy and the pain of love. If you wipe out that memory and that pain, you wipe away some of your deep humanity. A spotless mind and its "eternal sunshine" are not something to be coveted. We are forever changed--and deepened--by the great joys and utter miseries of our lives with others...it MAKES us who we are. You have to let people in, even repeatedly, as Clem & Joel do, to experience, and become, and BE, the humans we are meant to be.