define dag in the context of airflow (apache#46875)

* define dag in the context of airflow

* clean up and make common docs reusable

* fix failing check

docs/apache-airflow/core-concepts/dags.rst

@@ -20,7 +20,9 @@
 DAGs
 ====
 
-A *DAG* (Directed Acyclic Graph) is the core concept of Airflow, collecting :doc:`tasks` together, organized with dependencies and relationships to say how they should run.
+.. include:: ../../exts/includes/dag-definition.rst
+    :start-after: .. dag-definition-start
+    :end-before: .. dag-definition-end
 
 Here's a basic example DAG:
 
@@ -30,6 +32,9 @@ It defines four Tasks - A, B, C, and D - and dictates the order in which they ha
 
 The DAG itself doesn't care about *what* is happening inside the tasks; it is merely concerned with *how* to execute them - the order to run them in, how many times to retry them, if they have timeouts, and so on.
 
+.. include:: ../../exts/includes/dag-definition.rst
+    :start-after: .. dag-etymology-start
+    :end-before: .. dag-etymology-end
 
 Declaring a DAG
 ---------------

docs/apache-airflow/index.rst

@@ -33,6 +33,13 @@ code" serves several purposes:
 - **Extensible**: The Airflow® framework contains operators to connect with numerous technologies. All Airflow components are extensible to easily adjust to your environment.
 - **Flexible**: Workflow parameterization is built-in leveraging the `Jinja <https://jinja.palletsprojects.com>`_ templating engine.
 
+DAGs
+-----------------------------------------
+
+.. include:: ../exts/includes/dag-definition.rst
+    :start-after: .. dag-definition-start
+    :end-before: .. dag-definition-end
+
 Take a look at the following snippet of code:
 
 .. code-block:: python
@@ -78,6 +85,10 @@ seen running over time:
 Each column represents one DAG run. These are two of the most used views in Airflow, but there are several
 other views which allow you to deep dive into the state of your workflows.
 
+.. include:: ../exts/includes/dag-definition.rst
+    :start-after: .. dag-etymology-start
+    :end-before: .. dag-etymology-end
+
 
 Why Airflow®?
 =========================================

docs/exts/includes/dag-definition.rst

@@ -0,0 +1,32 @@
+ .. Licensed to the Apache Software Foundation (ASF) under one
+    or more contributor license agreements.  See the NOTICE file
+    distributed with this work for additional information
+    regarding copyright ownership.  The ASF licenses this file
+    to you under the Apache License, Version 2.0 (the
+    "License"); you may not use this file except in compliance
+    with the License.  You may obtain a copy of the License at
+
+ ..   http://www.apache.org/licenses/LICENSE-2.0
+
+ .. Unless required by applicable law or agreed to in writing,
+    software distributed under the License is distributed on an
+    "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+    KIND, either express or implied.  See the License for the
+    specific language governing permissions and limitations
+    under the License.
+
+.. dag-definition-start
+A DAG is a model that encapsulates everything needed to execute a workflow. Some DAG attributes include the following:
+
+* **Schedule**: When the workflow should run.
+* **Tasks**: :doc:`tasks </core-concepts/tasks>` are discrete units of work that are run on workers.
+* **Task Dependencies**: The order and conditions under which :doc:`tasks </core-concepts/tasks>` execute.
+* **Callbacks**: Actions to take when the entire workflow completes.
+* **Additional Parameters**: And many other operational details.
+.. dag-definition-end
+
+.. dag-etymology-start
+.. note::
+
+    The term "DAG" comes from the mathematical concept "directed acyclic graph", but the meaning in Airflow has evolved well beyond just the literal data structure associated with the mathematical DAG concept.
+.. dag-etymology-end