Move Object in Button Click smooth to position?

By the nature of your function name (Clicked: past tense, singular), you want a single process to be started and manage itself from the time of your click. The way to accomplish this is a Coroutine.

 void Clicked()
     {
         // Get the target position
         Vector3 relativeLocation = new Vector3(0, -10, 0);
         Vector3 targetLocation = Pic.transform.position + relativeLocation;
         float timeDelta = 0.05f;
 
         // Start your coroutine
         this.StartCoroutine(SmoothMove(targetLocation, timeDelta));
     }
 
     IEnumerator SmoothMove(Vector3 target, float delta)
     {
         // Will need to perform some of this process and yield until next frames
         float closeEnough = 0.2f;
         float distance = (Pic.transform.position - target).magnitude;
 
         // GC will trigger unless we define this ahead of time
         WaitForEndOfFrame wait = new WaitForEndOfFrame();
 
         // Continue until we're there
         while(distance >= closeEnough)
         {
             // Confirm that it's moving
             Debug.Log("Executing Movement");
 
             // Move a bit then  wait until next  frame
             transform.position = Vector3.Slerp(Pic.transform.position, target, delta);
             yield return wait;
 
             // Check if we should repeat
             distance = (Pic.transform.position - target).magnitude;
         }
 
         // Complete the motion to prevent negligible sliding
         Pic.transform.position = target;
 
         // Confirm  it's ended
         Debug.Log ("Movement Complete");
     }

edit: Changed transform.position to Pic.transform.position, as poster had.

I would suggest looking into "Vector3.Lerp" here is the unity documentation about it:

http://docs.unity3d.com/ScriptReference/Vector3.Lerp.html

Here is how you would use it:

 transform.position = Vector3.Lerp(<FROM_POSITION>, <TO_POSITION>, <CALC_DISTANCE>);
 
 Inside <CALC_DISTANCE> this variable could account for your speed or a distance variable like they do in the example.

The example they provide is amazing. Click on the link and check it out. The Vector3.Lerp will smoothly transition from one point to another just like you want. This would most likely be called on an update function and have the "" be the current position of the person you are moving.

EX:

 this.transform.position

So here is a complete example that you could use:

 transform.position = Vector3.Lerp(transform.position, target.position, speed * Time.deltaTime);