1. The meaning: the speaker is craving for Celia's love. He wants to quench his thirst not with an actual drink, but with Celia's looks and kisses. In these lines, he confirms that his desire is not only a physical (or even a mortal) one. It is also spiritual and emotional, and can only be satisfied with "a drink divine". He would prefer to drink from Celia's cup that from Jove himself. Jove of Jupiter was the most powerful god in the Roman mythology.
2. Literary devices: the soul's thirst is a metaphor for the speaker's needs and desires regarding Celia. Likewise, "a drink divine" is a metaphor for love, eroticism, everything that the speaker craves for. Those two metaphors correspond with each other: just like a thirsty person needs a drink, so an enamored person needs love (a look, a kiss) of their beloved. Nectar is a mythological drink of gods. Here, it serves as a hyperbole: even nectar, supposedly the most intoxicating drink, is nothing compared to Celia's love.
