Two cookies are used by this site. The essential one is the session cookie, usually called TotaraSession. 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 TOTARAID. 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.