"A Red, Red Rose" is about a kind of love that will outlast even the destruction of the earth—the evaporation of the seas, the melting of rocks. It is a love so strong that the speaker would have no problem walking ten thousand miles to be back with his "bonnie lass." It's not just love, but "love, love."
And what do we associate most with love? Roses. Especially red ones. We buy them for significant others on Valentine's Day and other occasions. We pin them on would-be suitors' lapels. We strew their petals down wedding aisles. You can't go wrong with roses, you might say. But the rose in the title isn't just a red one; it's a red, red one. It's really red. Really, really red. That repetition reminds us that this dude is not playing around. His love is no joke, lest you write him off as another lothario.