An HTTP cookie (also called web cookie, Internet cookie, browser cookie, or simply cookie) is a small piece of data sent from a website and stored on the user's computer by the user's web browser while the user is browsing. Cookies were designed to be a reliable mechanism for websites to remember stateful information or to record the user's browsing activity (including clicking particular buttons, logging in, or recording which pages were visited in the past).
The essential one is the session cookie, something like ******Session. You must allow this cookie into your browser to provide continuity and maintain your login from page to page. When you log out or close the browser this cookie is destroyed (in your browser and on the server).
The other cookie is purely for convenience, usually called something like ******ID. It just remembers your username within the browser. This means when you return to this site the username field on the login page will be already filled out for you. It is safe to refuse this cookie - you will just have to retype your username every time you log in.