Network partitions happens when multiple parts of a cluster become separated due to some type of network failure, whether permanent or temporary. Often temporary failures heal spontaneously, within a few seconds or at most minutes, but the damage that can occur during a network partition can lead to inconsistent data. Closely tied to Brewer's CAP theorem, distributed systems choose to deal with a network partition by either sacrificing availability (either by shutting down or going into read-only mode) or consistency by allowing concurrent and divergent updates to the same data.
Network partitions are also commonly known as a Split brain, after the biological condition of the same name.
For more detailed discussion, see this blog post.