Cookies work in web browsing by storing small pieces of data on a user's device, which can be retrieved by websites during future visits. They help enhance the browsing experience by remembering user preferences, login credentials, and shopping cart contents. When a user visits a website, the site can access its cookies to provide personalized content and features. However, cookies also raise privacy concerns, as they can track user behavior across different sites. Web browsers typically offer options to manage cookie settings, allowing users to control their data and enhance their online privacy.