The desire that this poem explores can be interpreted in multiple ways. Literally, the narrator is talking about drinking wine and eating fruit. However, metaphorically these images could represent ambition, sexual desire, and experience in general.
In this metaphor, “thirst” represents the longing for drink and “wine” represents the fulfillment of that desire. The narrator claims that “no wine” is as great as the experience of “thirst” to suggest that longing is more fulfilling than the actual fulfillment of desire.