Airflow is a workflow engine from Airbnb. Airbnb developed it for its internal use and had recently open sourced it. In Airflow, the workflow is defined programmatically. Airflow document says that it's more maintainable to build workflows in this way, however I would leave it to the judgement of everyone. A developer, anyway would love anything programmatic. :) Airflow comes with a UI also and I can say that the UI is very clean and impressive.
The main concept of airflow is a DAG (Directed Acyclic Graph). Yes, it's the same graph that you have seen in Maths, if you have seen it. A DAG contains vertices and directed edges. In a DAG, you can never reach to the same vertex, at which you have started, following the directed edges. Otherwise your workflow can get into an infinite loop. In workflow context, tasks can be defined as vertex and the sequence is represented with the directed edge. The sequence decides the order in which the tasks will be performed.