Parenting, grouping, and hierarchy
Parenting When you parent object A to object B, the transformation of object B is applied to objects A and B, while the transformation of object A is applied to object A alone. For instance, if you scale object B, object A will be scaled, according to the scaling applied to object B, whereas if you scale object A, object B will not be affected by that. Object A is called a "child" and object B is called a "parent".

Parenting in Maya

Select an object to be a child first, and shift-select an object to be the parent second, and Edit -> Parent or 'p'
Grouping When you create a group with multiple objects (or a single object), the transformation applied to the group is applied to every member in the group. Grouping is like parenting objects (or an object) to a null parent.

Grouping in Maya

Select objects to be grouped and Edit -> Group or Ctrl+g
Hierarchy Objects in 3D space that are parented together create a hierarchical structure. The object at the top level is called the "root". Each object, except for the root, in a hierarchy must have one parent object and has an arbitrary number of child objects.
Hierarchy in Maya Window -> Hypargraph... opens Hypergraph which lists all the objects in hierarchical structures.