Optima dies…prima fugit
This quote comes from the Georgics, an instructive poem written about farming by the epic Roman poet Virgil and translates to "The best days…are the first to flee." Jim studies Virgil when he's away at college and specifically mentions this line at the end of Book 3, Chapter 2. Let's take a look at the passage:
As I sat down to my book at last, my old dream about Lena coming across the harvest-field in her short skirt seemed to me like the memory of an actual experience. It floated before me on the page like a picture, and underneath it stood the mournful line: "Optima dies ... prima fugit."
There are two major connections to My Ántonia in this epigraph. The first is the actual content of the line – the best days are the first to flee. My Ántonia is a romanticized look back at the past, and the transience of youth is a major theme in the novel. Jim in particular is enamored of long-gone better days. (Remember that the novel is itself his memoir and so is all about the past.)
The second connection has to do with the source of this quote, the Georgics. In this lengthy poem, Virgil discusses the virtues of the farming life while teaching his readers the best way to live off the land. The relationship between man and the natural world is another central theme in My Ántonia. Part of the romantic veneer of Jim's memoir has to do with his admiration for the vast, beautiful open spaces of the Nebraska landscape.
There is also a connection here to Cather's own life, because she studied Latin and Greek herself both in high school and in college (source). We can see Cather's own love for these ancient languages reflected in Jim's passion, and of course in this choice of epigraph.