What occurs when a website can know enough about a person's likes and dislikes that it can fashion offers that are more likely to appeal to that person?

Answer: Personalization

Explanation: Personalization technique in the websites is approach towards any individual in which he/she can describe their like or dislike and gets to know about the user's need by which they search for any particular fashion, their history of search etc. In this the person displays their liking and the websites starts to display those content which are appealing to the particular user.