Legacy Documentation: Version 4.3.0
Vector3.SmoothDamp
static function SmoothDamp(current: Vector3, target: Vector3, currentVelocity: Vector3, smoothTime: float, maxSpeed: float = Mathf.Infinity, deltaTime: float = Time.deltaTime): Vector3;
static Vector3 SmoothDamp(Vector3 current, Vector3 target, Vector3 currentVelocity, float smoothTime, float maxSpeed = Mathf.Infinity, float deltaTime = Time.deltaTime);
static def SmoothDamp(current as Vector3, target as Vector3, currentVelocity as Vector3, smoothTime as float, maxSpeed as float = Mathf.Infinity, deltaTime as float = Time.deltaTime) as Vector3
Parameters

current The current position.
target The position we are trying to reach.
currentVelocity The current velocity, this value is modified by the function every time you call it.
smoothTime Approximately the time it will take to reach the target. A smaller value will reach the target faster.
maxSpeed Optionally allows you to clamp the maximum speed.
deltaTime The time since the last call to this function. By default Time.deltaTime.
Description

Gradually changes a vector towards a desired goal over time.

The vector is smoothed by some spring-damper like function, which will never overshoot. The most common use is for smoothing a follow camera.
	// Smooth towards the target
	var target : Transform;
	var smoothTime = 0.3;
	private var velocity = Vector3.zero;
	
	function Update () {
		// Define a target position above and behind the target transform
		var targetPosition : Vector3 = target.TransformPoint(Vector3(0, 5, -10));
		
		// Smoothly move the camera towards that target position
		transform.position = Vector3.SmoothDamp(transform.position, targetPosition,
		                             velocity, smoothTime);
	}

using UnityEngine;
using System.Collections;

public class Example : MonoBehaviour {
    public Transform target;
    public float smoothTime = 0.3F;
    private Vector3 velocity = Vector3.zero;
    void Update() {
        Vector3 targetPosition = target.TransformPoint(new Vector3(0, 5, -10));
        transform.position = Vector3.SmoothDamp(transform.position, targetPosition, ref velocity, smoothTime);
    }
}

import UnityEngine
import System.Collections

public class Example(MonoBehaviour):

	public target as Transform

	public smoothTime as float = 0.3F

	private velocity as Vector3 = Vector3.zero

	def Update() as void:
		targetPosition as Vector3 = target.TransformPoint(Vector3(0, 5, -10))
		transform.position = Vector3.SmoothDamp(transform.position, targetPosition, , smoothTime)