1. _root
   _root is an alias, just as _parent and this. It is used to access the root of the current level. For instance, if you write this in the first frame of your movie:

MovieClip.prototype.whichRoot = function () {trace (_root);} _root.createEmptyMovieClip("firstClip",1); firstClip.createEmptyMovieClip("secondClip",1); firstClip.secondClip.whichRoot(); // returns _level0
 

Quite normal, since the default level is 0. But if you load a movie in _level1, and if that movie is referring to _root, it will mean _level1. So be careful about that: to access the _root of the master movie from the loaded movie, you have to write:

_level0._root.myVariable = ...

2. _parent
   OK, now _parent is quite similar, except it refers to the clip that is one "layer" higher in the tree. In this example, _root creates (hence contains) firstClip, so it is his parent, firstClip creates secondClip, which creates thirdClip:
    

MovieClip.prototype.whichParent = function () {trace (this._parent);} _root.createEmptyMovieClip("firstClip",1); firstClip.createEmptyMovieClip("secondClip",1); firstClip.secondClip.createEmptyMovieClip("thirdClip",1); firstClip.whichParent(); // returns _level0, aka _root firstClip.secondClip.whichParent(); // returns _level0.firstClip firstClip.secondClip.thirdClip.whichParent(); // returns _level0.firstClip.secondClip
 

3. this
   this refers to the current object. It is particularly useful in Flash MX when you build a prototype, as we will see later.
   It is also vital now that Flash handles variables scope differently. In Flash 5, declaring a variable in an onClipEvent(enterFrame) made the variable relative to the clip. It's over now, since all the variables left alone are relative to the current timeline. That's why if several objects use the same method, prototype or function at the same time, they can all modify the same variables, so the animation cannot run normaly.
   That's why you have to tell Flash when your variables depend on the current object by declaring them as part of this:

   onClipEvent (enterFrame)
   {
        this.myVar = 5;
   }

   If you hadn't put this, and that there was a variable called myVar on the _root, this variable would have been replaced by that one. You see the problem?