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);

using UnityEngine;
using System.Collections;

public class Example : MonoBehaviour {
    void Example() {
        transform.localPosition = new Vector3(0, 0, 0);
        print(transform.localPosition.y);
    }
}

import UnityEngine
import System.Collections

public class Example(MonoBehaviour):

	def Example() as void:
		transform.localPosition = Vector3(0, 0, 0)
		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.