Try this simple exercise:

1. Stand on both your feet, as you normally do when not walking.
2. Now, keeping your body straight, try to lean very slightly to your front, as much as your feet allow it without having to make a step. You should now feel your weight resting on your toes.
3. Now, lean as much as you can towards your back. Remember, your body should not bend in any way. You should now feel your entire weight on your heels.

Maintaining your axis is a very important thing when dancing tango. In fact, you should probably concentrate most of your attention in the beginning on how to step and how to pivot while keeping your wight on the right foot.
You wouldn't want to push or pull your partner and you wouldn't want him/her to feel as trying to move a door!

This is the beauty of it all when speaking about axis. You can lean on your toes and give him/her that perfect embrace he/she's been longing for and still allow your legs to have enough room in order to make the steps, the pivots and those nice adornos you've been admiring on YouTube.
Or you can simply lean towards your back to magnify your steps, to better feel the energy and put it into your best moves.

Now don't misunderstand! During a single song, you will probably switch between the two depending on where he may lead and on how she may want to shape it. The important thing is to keep in mind that between your toes and your heels is the place you want to keep your weight and your axis. Also remember that your partner has the same range to play with when it comes to his/her axis. Therefore, the most beautiful movements will probably derive from this game you are both playing.

There will be times when you will feel that you have pushed out of this range and lose your balance. Even if this is acceptable for the first few lessons, in time, you should learn to control your body as you please! "Really?" you may ask. Well, in fact, yes! After all, it is YOUR body we are speaking of and YOU of all people should be able to control it as you please. Yes, you may lose your balance. And yes, you may not be able to make that perfect pivot from the very first lesson. But that is all probably because nobody has really explained you how to do it. In your own terms.

The key to keeping your axis is the perfect balance between the energy you are receiving and the steps you are making (together with the shape you decide to give them). For example, when talking about a voleo, you can actually pinpoint the energy rising from the leader's torso, going through his arms into the follower's arms, upper body, leg and finally all the way through to her toes, giving the beautiful shape of a voleo.

What kind of exercises can you try for maintaining your axis?

Caminar - maintain at every step your toes, your torso and your forehead on the same vertical line.
Caminar with a counter balance - work in pairs. When you are walking to the front, your partner should push you to the back. You should be able to push him back and make a step in perfect balance. When you are walking to the back, your partner should push you forward. Work until you can make steps in perfect balance. You should be able to do that by finding the equilibrium between the energy of your partner's push and the energy you invest in the movement.
Pivot to the wall - take the wall as your partner and try to make 180 degrees pivots in perfect balance. At first, you will lean towards the wall to take the energy you need. In time, you should be able to let it go more and more and finally, do the pivots on your own. After that, play with the speed of the pivots and the adornos you can do.