I find this concept is important in understanding causal ordering for distributed systems, for example in the context of CRDTs. For events generated on a single device, you always have a complete ordering. But if you generate events on two separate devices while offline, you can't say one came before the other, and end up with a ≹ relationship between the two. Or put differently, the events are considered concurrent.

So you can end up with a sequence "d > b > a" and "d > c > a", but "c ≹ b".

Defining how tie-breaking for those cases are deterministically performed is a big part of the problem that CRDTs solve.