Vertigini translates to "vertigo" or "dizziness". It's an interesting word because it describes a physical sensation that can also be used metaphorically.
In the song, Biagio Antonacci uses it to describe the feeling of being with someone who is so extraordinary that they make him feel dizzy, as if she's so tall she touches the sky. He sings, "Le tue vertigini un sintomo d'altezza" (Your vertigo a symptom of height), implying her unique qualities are almost overwhelming.
"Ti Saprò Aspettare" is a quiet promise wrapped inside a love song. Biagio Antonacci sings about a woman who feels almost too much to take in: her smile becomes a kind of cage, and she's tall enough that she seems closer to the sky than to him. Instead of trying to change her, he decides to wait.
The chorus keeps the promise plain and repeated: I will know how to wait for you, there will be things to do, I will wait for you. It reads less like a grand declaration and more like a steady, everyday one, patience treated as its own form of love.
Later he watches her draw shapes in the dust, symbols she reads slowly and with effort, and notices that time doesn't really change her so much as explain her. The song closes on that same idea: whatever there is to work through, he'll still be there waiting.