Accarezzare means "to caress" or "to stroke". It's a beautiful and tender verb that evokes a sense of intimacy and gentle affection, making it more evocative than a simple "touch".
In Gino Paoli's song, he sings about "due mani da accarezzare" (two hands to caress). This highlights the deep appreciation and tenderness he feels for the person, emphasizing not just their presence but the loving interaction he desires, making it a very romantic and enticing word.
Gino Paoli spends the whole song thanking a woman for basic facts about her, and that's the trick of it. He thanks her "di esistere" (for existing), for having "due profondi occhi blu" (two deep blue eyes), for hands "da accarezzare" (to caress). Then the compliment gets bigger: "Grazie di non essere rimasta col sole e con le stelle" (thank you for not staying with the sun and the stars), as if she chose earth over the sky. By the last verse he isn't thanking her for anything she did at all, just "di esistere per me" (for existing for me).