Покохав means "fell in love." While it's a common concept, this specific verb form is interesting because it's the perfective past tense of кохати, which specifically refers to a deep, romantic love, often more profound than just любити (to like or love in a broader sense).
In the song, the very first line is "Я покохав тебе за перші поцілунки" (I fell in love with you for the first kisses), immediately setting the intensely romantic and passionate tone. It's a powerful and direct declaration of profound affection that perfectly encapsulates the song's theme.
"Покохав" (I Fell in Love) is KALUSH's confession of falling hard, and fast. The singer says it happened from their very first kiss, comparing her to a lighthouse guiding him through a storm.
From there he can't stop thinking about her. He imagines climbing to her window, lies awake at night, and keeps crossing the same streets hoping to run into her again. He admits he won't hold back his feelings, even guessing at her phone number and address just to find her once more.
By the end, what started as a passing thought feels certain. She is the one he pictured, and now she has become his whole life.