Final answer:
The device that allows website operators to track user behavior is called a cookie.
Step-by-step explanation:
The device that allows website operators to track how often a user visits a site, what he or she looks at while there, and in what sequence is called a cookie.
A cookie is a small piece of data that is stored on the user's computer by the website. It is used to remember user information and preferences, including past browsing behavior.
For example, when a user visits a website and logs in, a cookie is created to save their login information. This allows the website to recognize the user when they return and personalize their experience based on their previous actions.