Cookies are small text files stored on a user's computer that contain information about a user's browsing activity. They allow websites to store and retrieve information from the user's computer through their browser. There are three main types of cookies: name cookies that store a user's name for a personalized welcome message, password cookies that store a password for automatic logins, and date cookies that store a user's previous visit date. Cookies have advantages like being simple to implement and not requiring server resources, but also disadvantages like lack of security, size limitations, and ability for users to refuse or delete cookies.