Three cookies are used on sites powered by OCI.

The essential one is the session cookie, usually called MoodleSession. You must allow this cookie in your browser to provide continuity and to remain logged in when browsing the site. When you log out or close the browser, this cookie is destroyed (in your browser and on the server).

The other cookies are purely for convenience. The first one is usually called MOODLEID or similar. It just remembers your username in the browser. This means that when you return to this site, the username field on the login page is already filled in for you. It is safe to refuse this cookie - you will just have to retype your username each time you log in. The second one is called lastusedtheme or similar. It is just used to remember which theme you last viewed (for multi-site environments that offer different themes based on the site you are visiting). It is safe to refuse this cookie - you will just be redirected to the site's default theme.