Internet cookies, or HTTP cookies, are text objects sent by web servers to browsers to identify users and remember information like items in a shopping cart or login details. There are various types of cookies, including session, persistent, secure, HTTP only, third-party, and zombie cookies, each serving different purposes related to data security and user tracking. Cookies have several applications, such as session management and personalization, but they also have limitations, including privacy concerns and the ability to delete them from browsers.