The essential one is the session cookie, usually called 'MoodleSession'. 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, for example, 'MOODLEID', or similar. It just remembers your username within the browser (if you select 'Remember username' option). This means that 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 if you wish - you will just have to retype your username every time you log in.
For further information please contact us - details here.
Cookie Statement v.1 (January 2014)