A cookie is a small data file which is stored on your PC by a website. The next time you enter that site, it examines the data on the cookie and uses it to customise the site according to any previoulsy specified preferences. For example, a new site would recognise that you wnted only sports and politics news and adjust it's articles accordingly.
They are usually benign and often useful, nothing Big Brother about them at all. You can finc them in your Internet Cache but they are usually not flushed. in IE go to Tools-Internet Options-General Tab-Temporary Internet Files-Settings-View Files where you can delete them if you wish.