Cookies are extremely small, harmless text files which your web browser stores on your computer. They are designed to be supplied only to the website who sent the cookie in the first place, and are generally used to tailor the user experience specifically to you, for example, to deliver a list of items in your shopping basket.
Generally yes, but bear in mind that this will negatively affect your user experience. Instructions on how to do this vary significantly from browser to browser. More information can be found on the "All About Cookies" website: