We're currently considering it as a self-hosted process engine to automate technical business processes and to coordinate a few automation systems like jenkins. Crap like, trigger a database restore via system A, wait until complete, update tickets, trigger some data migration from that database via System B, update tickets. Maybe bounce things back to human operators on errors and wait for fixing / clarification. Trigger a bunch of deployments in parallel and report on success.
Systems in this space are either (a) huge, hugely expensive enterprise applications designed to consume all business processes, which is a bit overkill for our current needs (Camunda, SAP, Stackstorm, ...), (b) overfitted onto a very specific data analysis setup (aka: if you don't have hadoop, don't touch it) or (c) overly simplistic and offering no real benefit beyond investing into self-hatred, guiness and making jenkins work.
Airflow seemed like a bit of a decent middle ground there for workflows a bit beyond what you can sensibly do via jenkins jobs.