to feel attracted to or drawn to someone or something; to be fascinated by something.
彼女の優しい声に心惹かれた。
I was drawn to her gentle voice.
古い町並みの静けさに心惹かれて、写真をたくさん撮った。
I was fascinated by the calm of the old streets and took many photos.
彼の誠実さに心惹かれる人が多い。
Many people are attracted to his sincerity.