Quorum is the name given to a mechanism which is intended to help solve the SplitBrain problem, by selecting no more than one ClusterPartition when failures in cluster communication cause the cluster to split into multiple ClusterPartitions.
Once a ClusterPartition is selected to have quorum, that partition can run services for the cluster.
The most well-known method of awarding quorum to a ClusterPartition for an n-node cluster for quorum is to award quorum to that partition which has more than n/2 nodes in it.
Of course, this causes problems for the case where n is 2, since any failure at all will cause the entire cluster to shut down.
To aid in this problem, there are a variety of other methods available to compute quorum, or break ties in quorum voting.
In Linux-HA, we provide a QuorumDaemon to help resolve this situation.