To bedazzle is to charm or impress someone, sometimes to the extent that they feel confused or overwhelmed. A charismatic speaker might bedazzle her audience so much that they all want to buy her new book.
Something can literally bedazzle you, or blind you a little bit: the sun glinting off the ocean around your sailboat might bedazzle you. It's more common, however, to find this verb used in a figurative way, when a person amazes or impresses you. The root of bedazzle, the Middle English dasen, or "daze," possibly stems from the Middle Dutch word of the same spelling, which means "act silly."