This song, so famous in English, is a classic and fascinating expression of love. Jonson's ideas are so sincere and unusual that they are memorable as well as beautiful.
"Drink to me only with thine eyes" means Ben is asking his beloved to look at him with love. He doesn't want her to proclaim her love to him with a toast ("drinking to him"), but with a glance. He is asking for an expression of love in unconventional ways--- a look, or a "kiss within the cup" (and how, exactly, can a kiss be left anywere?). He will "not ask for wine" if she does this, meaning that a look, or even a promised kiss from her, is far greater than any sweetness he could get from drinking wine.
Building on the wine metaphor, Jonson now compares love to a "thirst that from the soul doth rise" -- a hunger of the soul for love, rather than a bodily longing for something to drink. This is a neat comparison, and elevates the expression of his love from something merely physical to something that comes from the "soul". This thirst needs a "divine" drink -- implying that love from his lady is such a great thing that it is better than "Jove's nectar" (the Olympian gods of Greece, of whom Jove (Jupiter, or Zeus) was the head, did not eat and drink normal food, but rather had divine food and drink called ambrosia and nectar -- supposedly the most wonderful food imaginable, which gave eternal life!)
Jonson continues the divine, or supernatural, metaphor by saying that he has sent her wreath of roses, not just to honor her beauty, but to preserve it forever. This could be, he claims, attained by her breathing on the flowers. Her divine breath, perhaps again like the breath of the Olympian gods, would render the roses immortal. The last lines claim that this would also mean that the roses would no longer smell their own sweet smell, but something infinitely sweeter: her.
Within this last metaphor of divinity and immortality are contained some of the ideals of Renaissance love. Love was supposed to be likened, in many ways, to divine love, and the closer it approached it the greater the love was. Also, the hope of the endurance of love, such as the imperishable roses, would be part of a love poem such as this. Jonson takes seemingly simple ideas -- eyes, wine, a kiss, a cup, and roses -- and makes them into a sophisticated and moving tribute of love desired, and, perhaps, attained.