There will never be a step, sequence, or trick in tango that will come close to matching the power of the embrace --Ney Melo.

So, what is the point of the embrace? Well, the first answer would be that we cannot single out one point above all. But here are a few candidates:

1. To connect the partners into a new entity - "The Couple"
2. To channel information from the leader to the follower and the other way around
3. To secure the necessary space under and around the partners, in relation to the other couples dancing around
4. To generate on one side energy and on the other side comfort for the two partners
5. To socialize and make the best of your expensive perfume

In more detail ...

1. There are countless exercises that improve the connection in a couple. Here are a few notes though: the Tango connection is a peculiar combination of rigidity and flexibility. The upper bodies of the partners should always face, as well as the hips. The trouble is these two elements rarely coincide, which will lead all the time to serious torsion from both the leader and the follower. Picture two enemy tanks engaged in battle, at close range, circling each other, while their turrets attempt to point the gun on each other. Both their drivers and their gunners attempt to adapt their gears but their reference is different. The driver adapts to the other's direction, while the gunner adapts to the other's position. In a Tango couple, the hips are the drivers and the upper bodies are the gunners.
The responsibility of maintaining the embrace is shared between the two partners, but not symmetrically. In this sense, the follower can be seen as the "mobile" part of the embrace, who always attempts to come back in front of the leader, as best as she or he can. Conversely, the leader can be seen as the "fixed" part of the embrace, around which the follower gravitates. While the term "fixed" is quite arguable, the leader's body, together with his arms do represent the solid skeleton of the embrace, the space delimiter.

2. Apart for pleasant and entertaining conversation, the embrace is the most important communication channel in a Tango couple. And like any other piece of communication, we have one partner that is proposing it (generally the leader, by inviting a partner to the dance floor) and the other accepting (the follower, accepting the invitation and the proposed embrace).
In the tango embrace, beginners usually pin point the golden information spot somewhere on the leader's chest. It is a good paradigm, because:

• it prevents the leaders from using their hands in an exaggerated manner (since they must lead with the "golden spot", not with the hands);
• it causes torsion in both partners (basically each turn lead with the "golden spot" implicates torsion);
• it creates a direction automatism in the follower, relative to the golden spot.

It is also a bad paradigm, because it makes the two partners stare at the other's "golden spot". While some dancers actually encourage that, by wearing sexy tops, this practice altogether is misguided because it is utterly unusable in close embrace.
So, which is the golden spot after all? The truth is there is no such thing - not a general one any way. The information is divided between the torso, the hips and the arms. What should a follower look for? Here are a few hints:

• the forward / backward / sideways intention which is meant to cause the corresponding basic step (but does not necessarily come together with a similar step of the leader)
• the pivot which is shown as a turn of the leader's upper body (!! complete with his shoulders !!). The actual sensation is that of space opening in one direction or the other.
• the energy coming with a certain intention can mean a small step, a wide step, two steps, or stop right there!!
• a change of level can mean: up - "watch out, a quick sequence is coming", down - "ok, quick section over"; or, they can just mean "stay right there, don't move, I'm going to do a neat trick"
• a counter position - i.e. blocking the follower's movement at the peak of its energy - is usually used to create a "voleo"

Regardless of the type of embrace you are using, the follower should also be able to channel some pieces of information to the leader (for example when the leader is trying to move with his backside, the follower can somehow prevent him from bumping into another couple by using all the elements in the embrace).

3. As we already mentioned, the leader's embrace delimits the bounding box of the couple, in relation with the others. It is his responsibility to take care of this box, firstly by not bumping into other boxes and secondly by keeping the couple's movement bounded inside the box as much as possible.
It is also the leader's responsibility to give the follower enough space inside the box, in general, but also in particular, for each step he leads. For this, the leader's posture is capital - which is basically a straight vertical pose (not tense though), with only a tensed abdomen.

4. The Couple is like a mechanism filled with energy - which is not difficult to achieve in fact: just take a buddy by the hands and start spinning. The question is how to use this energy in an elegant and most importantly controlled manner. The Embrace is again the answer - because it is as much an energy relay as it is an information one. Through the embrace, the leader can give his or her partner the energy for the next movement, just as he or she can take away the energy, thus stopping the movement, or on the contrary, accept it and go along with the step. To do so comfortably is no easy task. Here are a few notes:

• the leader's left hand should hold a firm follower's right hand - and should reciprocate in firmness and steadiness. It should never cross the midpoint between the two partners, into the follower's space.
• the leader's right hand should not be used as a firm grip on the follower's back, nor should it be used as a handle at all. Moreover, it should be quite mobile and adapt all the time to the direction and distance given by the embrace.

5. We're gonna leave this one to you... :)