In the last 30 years most art historians have dated the painting, based on its stylistic qualities, to c. 1485–87.
The iconography of The Birth of Venus is very similar to a description of the event (or rather, a description of a sculpture of the event) in a poem by Angelo Poliziano, the Stanze per la giostra. The painting takes the motif of Venus Anadyomene, depicting the Greek myth of the birth of Aphrodite, virginal and fully grown, rising from the sea. She does this cyclically and thus is her virginity renewed. This motif was common in ancient Greece and survived over a thousand years intact so that it was easy for Boticelli to know of it in the 1480s.
There are several interpretations of this painting by Sandro Boticelli ranging from the Neoplatonic influence of the then current Rennaisance thinking, but as well in honor of the Medici patrons, or a painting produced for a wedding, an attempt by Botticelli to revive and fulfill an earlier painting of Venus rumored to have been ruined - a painting of Venus with the model being Alexander's mistress, Pankaspe, and the painter Apelles, and even Christian symbology of Eve before and after the fall. There is no one interpretation that clearly carries the day. There are no records which allow us to know what Boticelli intended for certain. You can read all this and more on Wiki's site for The Birth Of Venus. There is a related site, Venus Anadyomene.
For myself, I first saw a reproduction of this painting while learning mythology in grade school, well before eighth grade. This painting of The Birth of Venus (full grown from the sea as per one of her main origin myths) has been with me most of my life. You may notice that there is not much realism here: in the real world the shell would tip over, and Venus could not hold that pose very long either. While Boticelli could be and mostly was much more realistic in his work, in this case he may have been imitating early classical style on purpose, mimicking the pictures found on Greek vases, and creating a definite fantasy world in any case.
Treating the woman as if she rose from the sea sometimes works better than giving her gems or silver or golden rings. I should know because she once rose above my willing bed and draped me with seafoam and love.
Some years ago my poetry took on a mythic flavor and I became a character in my own poems, a mage, "the man of the Northern Wall". This apellation is not completely fictional. My middle name is Noordwal, a Dutch term for north wall, though in current Dutch it mainly means north bank as in riverbank. I was told that an ancestor, a Portugese Jew escaping the Inquisition, settled in a small Dutch town and took this name from where he settled, near the north wall of the town. I have thought for a long time that -wal meant wall, think my mother told me that. A linguist might say that my usage is no longer common, is an older usage, but then the Inquisition happened in Portugal a few centuries ago, right around the time the Moors lost control of the Iberian Peninsula and the Jews lost the modest protection given them by Islam. Now I write as this mage, my poetry persona.