Each failover group is for a specific virtualization type (like OpenVZ or Xen), and must contain at least two host systems that support that virtualization method. For failovers to actually work, all virtual systems must share the directories containing their filesystems or disk images, either via NFS, Cluster LVM or iSCSI.
When a failover group is set to automatic mode, Cloudmin will detect host systems that have failed and move virtual systems off them to new hosts in the group, where possible. This will only happen after a period of downtime that you can configure on a per-group basis.
Virtual systems can also be forcible failed off a down host using the Force Failover item on the left menu, or the failover-system API command.