Check Point supports two type of clustering, ClusterXL a proprietary Check Point mechanism and VRRP, which is an open standard. I'm assuming that you refer to ClusterXL cluster in your question.
Cluster members need to see each others in the same L2 network and it's not allowed to have any routing devices between them. Clusters should meet the following requirements: max. delay 30 ms, max. packet loss 2-3%
Cluster members communicate with cluster control packets, which are sent every 100ms by default (which is also the min. value). CCP packets can be sent in multicast, broadcast or unicast. Multicast is the default in regular clusters, but you can change the mode to broadcast. Scalable Platform appliances and VSX in VSLS mode work with unicast.
CCP packets are sent over the sync and cluster interfaces (except on SP appliances only over the sync link) and is responsible for synchronization and health checks.
ClusterXL cluster can work in high-availability or load sharing mode.
Synchronization
Synchronization happens over the sync-link. Full-sync happens when the cluster member boots and delta sync every time when new information is available. Some connections use delayed synchronization by default.
PNOTEs
ClusterXL cluster monitors its interfaces and critical processes via a PNOTE-mechanism (problem notification). PNOTEs are also called critical devices. It's very flexible method and also allows you to add own PNOTEs to be monitored. If a PNOTE goes down (interface, process...) the cluster member declares itself as down. This usually means that a fail over takes place.
When all PNOTEs report their states as OK, the machine will try to change its state to 'Active', depending on the cluster configuration (HA mode / LS mode) and states of the peer members.
With ClusterXL cluster it's almost impossible to get a split-brain situation.
Failover
When a cluster member stops receiving ccp packets from its peer, it starts so called probing to determine whether the problem is on its own interface or on peer side. If the member itself has a problem it sets itself to down state. In case the peer had an issue, the status will become Active Attention. In Active Attention state, the cluster member forwards traffic, but other cluster members are down.
Please see sk66527 for more information about recommended configuration for ClusterXL.