If you find that iCloud has stopped working suddenly (e.g. the spinning progress never stops), check for a notification in Notification Center to accept new terms and conditions for iCloud. Click on the notification to bring up the new terms and conditions. You'd need to review the new terms and conditions and agree to it before your iCloud access is restored.
If you do not see such a notification, you can try to sign in to iCloud.com on your web browser using your Apple ID. If necessary, follow the prompts to review and update your account settings, then review and agree to any new iCloud Terms and Conditions.