Celia
As in most Renaissance love poems, we don’t learn a lot about Celia specifically. We do know that she shares a social circle with the speaker, as he sees her from afar at a banquet. We also know that she does not return the speaker’s affections.
The speaker
The speaker is the poem’s protagonist. He attempts to persuade Celia to return his affections by extending elaborate compliments her way. However, he also draws on “carpe diem” rhetoric, reminding Celia of her mortality and suggesting that she should embrace love in order to transcend it.
God
Although Jonson never directly refers to the Christian God, he's there in the background of the poem as the one true source of eternal life. The speaker desires Celia, and sees her as almost divine in her capacity to restore life, yet the poem reminds us that only the truly "divine drink" (God's love) can satisfy the soul's desire for eternal life.
