The essential theme of "Nothing Gold Can Stay" is that the beauty in everything fades as it ages. The initial beauty of a flower is only "so an hour." After that initial flowering, the life of the plant becomes mature, but less beautiful. Frost begins the poem stating "Nature's first green is gold," which sets it up for the remainder of his statement. It's "her hardest hue to hold" onto during life. Perhaps the best image that can help to explain this is in the second to last line: "So dawn goes down to day." At dawn, the sky can be golden and beautiful. It is something to stop and watch. But the dawn only lasts for an hour or so, before everything looks about the same for the rest of the day, until dusk, which again is beautiful, but only lasts for a little while.
As far as allusions go, Frost mentions the Garden of Eden, where Adam and Eve lost their innocence when Eve took a bite of the forbidden apple. As such, Frost lends the sense of a loss of innocence to his poem. Each morning, the dawn loses its innocence to the events of the day and Spring's flowers and leaf buds lose their innocence to the events of the summer.