Transformations change an object’s position, size, and orientation without changing its shape. “Transform” is basically a fancy way of saying “move, scale, and rotate".
Transformations are relative to an object’s (or component’s) pivot point, and take place along/around either the world axes, object axes, or local axes.
In Maya, the transformations you make to an object are saved in a transform node. That is, Maya remembers that the object is rotated 32,0,5 degrees and moved -3,6.2,7 cm from its original position.
When you group objects together, each group remembers its own transformations. This lets you create hierarchical animations easily.