O my Luve's like a red, red rose
That's newly sprung in June: (1-2)
That all sounds nice enough… but Roses have thorns, which makes the speaker's comparison just a little strange. We can't help thinking that he is leaving open the possibility that maybe love, like roses, has its own nasty side.
So deep in luve am I:
And I will luve thee still, my dear,
Till a' the seas gang dry: (6-8)
Notice that the word "dry" rhymes with "I." The word "dry" conjures up a lot of associations. We associate it with things that are boring, passionless, or even lifeless (if an ocean dries up, most of the things in it will die). This is certainly an odd rhyme. Why might Burns want to draw that connection?
Till a' the seas gang dry, my dear,
And the rocks melt wi' the sun; (9-10)
Not to go all obvious on you, but Rocks are really hard; they often symbolize permanence, steadfastness, and endurance. They don't usually melt. The speaker suggests that even if the impossible happens—if the world ends and things like rocks start melting—he will still love his "bonnie lass." In other words, this just got real.