Dissetarmi comes from the verb dissetare, meaning "to quench one's thirst." It's a less common, more evocative word than simply "bere" (to drink).
In the song, Andrea Bocelli sings, "E tornerò a dissetarmi il cuore" (And I will return to quench my heart's thirst). He uses this beautiful metaphor to express a deep longing and need to return to his love, suggesting that only she can satisfy his emotional yearning.
"Sarà settembre" is a quiet love song about distance and patience. A wind carries a message telling the singer to go back to the one they love, and the anxieties of the moment will fade once she finally reaches out for him again.
The title line, "e sarà già settembre," uses the turn of summer into autumn as a stand-in for time passing. The singer knows the season will change and the wait may be long, but he holds onto the dream that never dies and trusts the silence between them won't last.
By the end the promise is simple: he won't lose himself, and he will find his way back to her, no matter how much time the wind carries away.