Position of the transform relative to the parent transform.
If the transform has no parent, it is the same as Transform.position.
// Move the object to the same position as the parent:
transform.localPosition = Vector3(0, 0, 0);
// Get the y component of the position relative to the parent
// and print it to the Console
print(transform.localPosition.y);
Note that the parent transform's world rotation and scale are applied to the local position when calculating the world position. This means that while 1 unit in Transform.position is always 1 unit, 1 unit in Transform.localPosition will get scaled by the scale of all ancestors.