A third-party cookie placed on your machine byat one site can be detected by the same site at a later time or by athe third party, so your browsing history is to some extent public. There are both HTML and Flash cookies, so if you wish to remove them delete both types.
Browsers such as Firefox can be set to a "private" mode in which cookies are deleted at shutdown. Cookies can also be deleted by the browser or by free tool such as CCleaner. Deleting cookies may require you to log into sites which had opened automatically before.