Strapparti comes from the verb strappare, meaning "to tear" or "to rip". The suffix -ti indicates "you" (informal).
In the song, the singer expresses intense emotion with the line "Vorrei strapparti il cuore" (I would like to tear your heart out). While it sounds violent, it's a common Italian idiom to convey deep heartbreak, betrayal, or an overwhelming desire to remove someone from one's thoughts or life due to pain. It's a powerful and dramatic expression of emotional turmoil.
Two people who used to be together run into each other by chance, and the whole song happens inside that small, awkward conversation. He asks how she is, whether she has found a place of her own, and says something kind about her dress. He almost did not recognise her because of the new haircut. On the surface it is polite catching up between strangers.
Underneath, nothing has moved on for him. He admits he spent a long time hunting for her phone number, that he once asked God for it, and that the feeling of seeing her again is making him nervous. He says he does not live alone without her: he cannot sleep, and when he wants to sleep he counts twenty drops into a glass through his tears. In his dreams they are still together.
The memory he keeps returning to is small and specific. One evening she hid his photo among her dolls so that Marco would not find it, and he never told her that Marco was a friend of his. That detail carries the whole story of how the relationship ended.
By the second half he stops performing. In the first chorus he wonders whether it is out of place to say he still loves her; in the last one he says it plainly, and adds that it is too late now. He asks her to leave rather than stay and be held back, and looks at his own goodbye face without needing a mirror to see it.