Describes positions in which the leader and follower entrust to each other their respective balances, creating a third, shared axis between them. In essence they 'lean' towards one another (apilado, which can create movements such as volcacas), or away from one another (colgadas). The former is found in all forms of tango; the latter is found primarily in tango nuevo.
A large part of the problem is in our imprecise use of the words 'balance' and 'axis.' This is not merely a semantic argument--there is a huge conceptual difference between the two terms, and it has lead to a great deal of muddled teaching. My purpose in this posting is to suggest a precise use for the concept of "axis," using principles and nomenclature from physics. I apologize in advance for the length.
First of all, an "axis" is not a property of an object in the same way that mass or color or shape is. An axis is an imaginary construct used to describe the space in which objects reside. Axes (plural of axis) may be assigned freely to aid in the physical analysis of objects and their movement through space.
For example, when discussing the rotation of the Earth, it is convenient to assign an axis that is an imaginary straight line through the Earth's poles,about which it rotates, and which moves along with the Earth as travels through space. The Earth really doesn't "have" an axis; it is an imaginary construct of the space in which the Earth resides. Assigning this axis to the Earth, however, provides a convenient frame of reference in which to analyze its rotation, and it is convenient to colloquially call this the "Earth's axis." In physics, we call these types of coordinate axes "body coordinates," because they stay assigned to the body in a consistent way as the body moves through space.
All objects, including dancers, can be assigned one or more axes about which their rotation can be described. Indeed, all objects can be assigned three mutually perpendicular axes about which three independent types of rotation can be described. (In sailing and aeronautics, these are often referred to as yaw, pitch, and roll.) Again, these axes are not unique, nor are they properties of the body. They can be assigned in any number of ways, some more convenient than others, to provide a frame of reference in which to analyze a body's rotation.
In the case of a dancer, the most common type of rotation (unless, perhaps,you work for Cirque de Soleil) is that which takes place around an imaginary line through the long dimension of the body, as in a pirouette. A convenient choice of axis with which to analyze this motion is the axis which extends through the ball of the pivoting foot up through the dancer's body and out through the top of the head. So, one often hears people refer to this as "the dancer's axis."
But this axis is not a property of the dancer. It is not something that the dancer "has," in the same way that a dancer has a particular weight, or posture, or hair color. It is a transitory construct that aids in the analysis of the dancer's rotation at the moment the dancer is rotating. One can talk about the axis of rotation of a ballet dancer doing a double pirouette in the air, a Tango dancer pivoting during an ocho, or a break dancer doing one of the those wild spins where they are upside down tucked in sort of a fetal position (how do they do that!). But there is nothing about the word axis that necessarily implies anything about posture, verticality, connection, balance, or even consistency of shape or frame. Indeed, during rotations, the shape of the dancer's body may change dramatically: think of an ice skater doing one of those incredible spins where they start in a sitting position crouched forward and end up standing and bending backwards.
So it makes no sense to talk about "being on your axis," or even to talk about axis, when there is no rotation nvolved. Michael Figart made a similar point.
I think that when teachers say "dancers need to be on their own axis," they actually mean a mélange of several different concepts, something like this: "You need to be on your own balance (this is debatable, by the way, but that is for another discussion), and you will find this easier if the shape of your body stays consistent, firm yet relaxed, with an upright posture that is vertical or close to vertical."
Now, if you are on your own balance, with consistent shape and upright posture, it is indeed easier to rotate or to be led in a rotation, as Igor Polk also pointed out. It can be very difficult to rotate when off balance, as any follow who has ever been yanked off her balance in the middle of pivoting during an ocho will attest, or as any lead can attest who as ever tried to lead a limp, bendy follow through an ocho. So, you could argue that it is correct to say, as a form of shorthand, that "dancers need to be on their own axis during rotations."
Yet even this more limited concept is not always true. In a colgata, both dancers are very much off of their individual balance, yet both are pivoting quite nicely around individual axes of rotation, which correspond roughly to the centerline of their bodies, and which are very much tilted from the vertical; and the couple is very much in balance and rotating quite nicely about a yet another axis that is vertical and extends through the shared pivot point, roughly where their two supporting feet are trying to share the same piece of real estate.
So, I think we need to be very careful about the use of the word "axis," because most of the time that it is uttered in a class, it is utterly meaningless. The same argument can be made with the term "energy," which is used all the time in dancing in ways that are so vague as to be, at best, completely useless, or, at worst, misleading. I will argue that we should drop all uses of the word axis except as it pertains specifically to describing the rotation of dancers in the act of rotating or pivoting.