Cookies function on websites as small data files stored in a user's web browser. They are used to remember information about the user, such as login credentials, preferences, and shopping cart contents. When a user visits a website, cookies allow the site to recognize the user on subsequent visits, enhancing the browsing experience by providing personalized content and smoother interactions. However, cookies can also raise privacy concerns, as they track user behavior across the web, prompting regulations and practices to ensure user consent and transparency in cookie usage.