It's a love poem, plain and simple. In fact, "A Red, Red Rose" just so happens to be one of the most famous love poems of all time, too. Nearly ever line in the poem says something about love, so it makes sense that this puppy has been slapped on more than its fair share of greeting cards.
Lines 1-2: Here it is, the most famous love simile ever. Or it's at least in the top five, right? The speaker's comparison of his love to a red, red, rose has gone down in history as pure romance.
Lines 3-4: The speaker says his love is like a "melodie" that's "play'd in tune." Since he uses the word "like," this comparison is a simile. Yep, another one.
Lines 5-6: The speaker says he is as "deep in love" as his "bonnie lass" is "fair." Since the word "as" occurs in this comparison, this is also a simile.
Lines 7-8: the speaker says he will love his "bonnie lass" until the seas dry up; the evaporation of the "seas" is a metaphorfor the end of the world—you know, something that can never happen (zombie apocalypses aside).
Lines 11-12: The speaker will be all about his lady love, at least while the "sands o' life shall run." "Sands of life" is a metaphor; one's time on earth is compared to something like an hourglass that has sand in it to measure time.
Lines 13-16: The speaker says farewell, and tells his "Luve" that he will return for her, even if he has to walk ten thousand miles.