What does the poet ask of Celia in "Song: To Celia"? Why?

If you drink to someone, you make them a toast and wish them well. The speaker asks Celia only to wish him well with the look in her eyes. He says:

Drink [a toast] to me only with thine eyes

He says this because he is deeply in love with Celia, and his soul has a thirst for being acknowledged by her. He states that he loves her so much he would not trade Jove's (the king of the gods) nectar for what he might see in her eyes.
This is courtly love poetry that plays with hyperbole or exaggeration. The poet says that just a kind look from her will sustain him. In the second stanza he states that simply having her breath on the wreath she returned to him (showing her rejection of his love) is enough to sustain him because it smells of her.