Sintonizza comes from the verb sintonizzare, meaning to tune in, synchronize, or harmonize. It's often used in the context of tuning a radio or TV.
In this song, it's used metaphorically in the line "Che sintonizza cuore ed anima" (That synchronizes heart and soul). It beautifully conveys the idea of a deep connection where two people's innermost beings are perfectly aligned, making it a unique and evocative choice.
Two people call each other late at night, after an evening where almost nothing was said. He opens gently, half apologising for waking her: if she is asleep, he will hang up. He only wants to know why she stayed quiet the whole time at the pizzeria.
The phone makes it easier, and the song knows it. You can say things down a phone line that you would never say to someone's face, especially once the whole city is asleep and nobody else is listening.
So it all comes out. She tells him to deal with it himself, that she is leaving, that she will erase him from her soul. He brings up her first boyfriend, the one he keeps running into near her house, and admits that what he is feeling sounds a lot like jealousy. Neither of them quite means the worst of it. Between the threats there are apologies, a promise to run over and kiss the tears away, and the small confession that he was being a bit stupid.
By the last verse it is nearly dawn, and the night has carried the jealousy off with it. Neither one will hang up first. They agree to count to three, and stay on the line anyway.