A person who's captivated is entranced or absorbed by something. A captivated child might stare with wonder at a tiny ladybug for many long minutes.
Use the adjective captivated to describe someone who is utterly charmed by something. A captivated student is enthralled by her teacher's history lesson, and a captivated audience is involved in every word spoken on stage during a play. The word is rooted in the Late Latin captivare, "to take or capture," which in turn comes from capere, "to seize." When something seizes your attention, you are captivated.