A woman's determination to attract a particular man. In the days when women's attire included head coverings, a woman who wanted to appeal to a man would wear her best bonnet. The phase was wellknown in the 18th century, when Jane Austen used it in Sense and Sensibility: “I abhor every commonplace phrase by which wit is intended; and ‘setting one's cap at a man,' or ‘making a conquest,' are the most odious of all.”