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.

Gradually changes an angle given in degrees towards a desired goal angle over time.

The value is smoothed by some spring-damper like function. The function can be used to smooth any kind of value, positions, colors, scalars. The most common use is for smoothing a follow camera.

	// A simple smooth follow camera,
	// that follows the targets forward direction
	var target : Transform;
	var smooth = 0.3;
	var distance = 5.0;
	private var yVelocity = 0.0;
	
	function Update () {
		// Damp angle from current y-angle towards target y-angle
		var yAngle : float = Mathf.SmoothDampAngle(transform.eulerAngles.y,
		                            target.eulerAngles.y, yVelocity, smooth);
		// Position at the target
		var position : Vector3 = target.position;
		// Then offset by distance behind the new angle
		position += Quaternion.Euler(0, yAngle, 0) * Vector3 (0, 0, -distance);
		// Apply the position
		transform.position = position;
		// Look at the target
		transform.LookAt(target);
	}

using UnityEngine;
using System.Collections;

public class Example : MonoBehaviour {
    public Transform target;
    public float smooth = 0.3F;
    public float distance = 5.0F;
    private float yVelocity = 0.0F;
    void Update() {
        float yAngle = Mathf.SmoothDampAngle(transform.eulerAngles.y, target.eulerAngles.y, ref yVelocity, smooth);
        Vector3 position = target.position;
        position += Quaternion.Euler(0, yAngle, 0) * new Vector3(0, 0, -distance);
        transform.position = position;
        transform.LookAt(target);
    }
}

import UnityEngine
import System.Collections

public class Example(MonoBehaviour):

	public target as Transform

	public smooth as float = 0.3F

	public distance as float = 5.0F

	private yVelocity as float = 0.0F

	def Update() as void:
		yAngle as float = Mathf.SmoothDampAngle(transform.eulerAngles.y, target.eulerAngles.y, , smooth)
		position as Vector3 = target.position
		position += (Quaternion.Euler(0, yAngle, 0) * Vector3(0, 0, -distance))
		transform.position = position
		transform.LookAt(target)