Understanding implicit in Scala

I was making my way through the Scala playframework tutorial and I came across this snippet of code which had me puzzled:

def newTask = Action { implicit request =>
taskForm.bindFromRequest.fold(
        errors => BadRequest(views.html.index(Task.all(), errors)),
        label => {
          Task.create(label)
          Redirect(routes.Application.tasks())
        } 
  )
}

So I decided to investigate and came across this post.

I still don’t get it.

What is the difference between this:

implicit def double2Int(d : Double) : Int = d.toInt

and

def double2IntNonImplicit(d : Double) : Int = d.toInt

other than the obvious fact they have different method names.

When should I use implicit and why?