We regularly get questions about how to set up a Galera cluster with just 2 nodes. The documentation clearly states you should have at least 3 Galera nodes to avoid network partitioning. But there are some valid reasons for considering a 2 node deployment, e.g., if you want achieve database high availability but have limited budget to spend on a third database node. Or perhaps you are running Galera in a development/sandbox environment and prefer a minimal setup.
Galera implements a quorum-based algorithm to select a primary component through which it enforces consistency. The primary component needs to have a majority of votes, so in a 2 node system, there would be no majority resulting in split brain. Fortunately, it is possible to add a garbd (Galera Arbitrator Daemon), which is a lightweight stateless daemon that can act as the odd node. Arbitrator failure does not affect the cluster operations and a new instance can be reattached to the cluster at any time. There can be several arbitrators in the cluster.