The essay begins with Asimov explaining the etymology of Valentine:
The Latin word valere means "to be strong", and from it we get such words as "valiant" and "valor", since one expects a strong person to be brave. We also get words such as "value" and "valid", since strength can refer not only to muscular power but also to something that finds its strength in being worth a great deal or in being true. In naming children, we can make use of words that imply the kind of character or virtue that we hope to find or instill in him or her. [...] The ancient Romans, by the same reasoning, might use the name "Valens", which means "strength". By the irony of history, such a name became particularly popular in the latter days of the Empire, when Rome had grown weak.
He then introduces a Roman emperor named Valens, a poor general who died while fighting the Goths at Adrianople. Valens had a brother who held the diminutive form of the name, "Valentiniatus". This diminutive form was popular, and is now shortened by English-speaking people to "Valentine". One martyr of the Catholic church, his feast day being 14 February, was St. Valentine. Having said all this, Asimov turns to the Roman holiday of Lupercalia -- celebrated on 15 February.
The ancient Romans had a holy spot where (according to legend) the wolf had suckled the twin brothers, Romulus and Remus, the former of whom eventually founded Rome. The spot was called "the Lupercal", from the Latin word lupus, meaning "wolf".
On that spot, every February 15, there was a festival held called the Lupercalia, during which animals were sacrificed. Thongs were prepared from the bloody strips of animal hide, and priests ran through the crowd striking out with those thongs. Those who were struck were considered to be cured of sterility. Naturally, those who wanted children flocked to the festival. Afterwards, I imagine, they engaged in those activities that were expecting to give rise to children -- striking while the iron was hot, so to speak. Consequently, the lupercalian festivities were associated with love and sex.
In 494, Pope Gelasius I forbade this pagan festival, but that sort of thing does no good. The festival simply continues under another name. For example, the celebration of the winter solstice was forbidden, but it still continues with almost all the pagan customs of the ancient Romans -- under the name of "Christmas". To the celebration of the vernal equinox was added the Christian feast of the resurrection, which became "Easter", and so on.
The Lupercalian festival of February 15 simply became St. Valentine's Day of February 14. Legends arose later to the effect that St. Valentine had been kindly to lovers, but that is undoubtedly just a cover for the good old fertility rites that have always been popular (and, I strongly suspect, always will be).
He ends the essay by commenting on the trivialization of the holiday by the greeting card industry. You can find the full essay in The Tyrannosaurus Prescription by Asimov, or in the forward to Fourteen Vicious Valentines.