O my Luve's like a red, red rose
That's newly sprung in June: (1-2)
So wait a second. Does this mean that the speaker's love can, like a flower, only bloom in spring, when the conditions are just right? That doesn't quite jive with the speaker's later emphasis on the immortality of his love, now does it? Here it seems like his love is subject to the forces of time.
And I will luve thee still, my dear,
Till a' the seas gang dry: (7-8)
That's more like it. Here he's all, yep, my love is timeless. Take that, you ocean.
Till a' the seas gang dry, my dear,
And the rocks melt wi' the sun; (9-10)
Maybe we should imagine that the rocks are a symbol of the speaker's everlasting love; they are hard and durable, and it'll be a long time before they melt (and a long time before his love wanes, if it ever does).
I will luve thee still, my dear,
While the sands o' life shall run. (11-12)
While "run" can just mean "pass" or "move," the word makes us imagine time passing by very quickly. This gives the poem a sense of urgency; the speaker acts, almost, as if he doesn't have a whole lot of time and must make haste.