The DAG hierarchy (also known as an object hierarchy) refers to the parent-child relationships of all nodes that make up an object. DAG stands for "directed acyclic graph". In essence, the DAG is a breakdown of how an instance of an object is constructed from a piece of geometry.
An object's DAG hierarchy always includes two types of nodes, transforms and shapes.
When you create a polygon sphere, for example, you can see in the Attribute Editor that it includes a shape node and a transform node. The shape node has attributes to define the geometry, while the transform node contains attributes that control the sphere's position, scale, or rotation. The shape node is the child of the transform node.
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