"A Red, Red Rose" is a ballad written in four quatrains (four stanzas composed of four lines each). The first and third lines of each stanza are written in iambic tetrameter (tetra - four stressed syllables). These lines stray a bit from strict iambic prosody, but for the most part the entire poem sticks to the iamb which is the pattern of an unstressed syllable followed by a stressed syllable. The second and fourth lines follow iambic trimeter which uses three stressed syllables.
O my Luve's like a red, red rose,
That's newly sprung in June;
The stressed syllables are: O, Luve's, red, rose, / new-, sprung, June. The musical quality of rhythm is important in this poem because it is about time as much as it is about love.
In the first stanza, the speaker uses simile to compare his love to a "red, red rose, / That's newly sprung in June." The love he has is fresh, new, and bursting with life. "Red" is repeated to underscore the idea that his love is at its brightest. Given that his love is at its most powerful, being "newly sprung in June," the indication is that this is temporary. Just as the rose's color will fade, his love is subject to the same decay.
It is also harmonious and musical like a song "sweetly played in tune." One could say that a song is timeless but the song itself, having a beginning and end in time, is also temporary.
The speaker, recognizing that his love might fade, reassures his beloved saying he will love her "Till a' the seas gang dry." Seemingly, this will be a long time, perhaps until the end of the world. But he doesn't say "forever." So, there may be some indication that even a love as powerful as this has, like the rose and the song, a limit in time.
Again, the speaker reassures his beloved that he will love her "While the sands o' life shall run." This could mean he will love her for all time or until the end of her or his life. What seemed like a very simple poem about love becomes a philosophical inquiry on time and the question of how love exists in time. Does time limit love?
In the last stanza, the speaker announces that he will be away from his beloved for "a while" indicating that he will return, but we have no idea how long "a while" really is. However, he says he will return even if he must travel ten thousand miles.
One could say that the speaker is simply making a pledge that although his love brief (like a newly sprung rose), it is also long-lasting. In other words, maybe it (love) only seems brief because it is experienced in time. Perhaps the speaker is trying to conceive of how to extract this brief moment of vibrant love from time itself, so that it would not be limited by the confines of time. In a modern context, this could be interpreted as wishing to extend the initial "falling in love" feeling longer than the limited time it tends to have.