Very simply, the theory is for the leader to influence the lady in such a manner that she moves in a very natural manner. The lead comes from many different places and is interpreted by the lady as a single feeling, creating a specific movement or action. The goal is to move and act as a single two-headed four-legged animal (a single complete moving entity).
There are specific rules that accommodate four-legged movement. These rules are what define a "Trained Dancer". A "Trained Dancer" is educated in the rules that allow the leaders actions to be intercepted and translated into natural movements by the lady. Normally we don't think of these actions as rules. There are also two-legged rules that we all follow but don't really think of as rules. As a two-legged animal, to walk forward across a room, I must follow the rule to "put one foot in front of the other". If I step sideways or step together, I don't progress across the room. When you are four-legged, there is a different set of rules. The "partners being offset from each other in closed dance position" would be a four- legged rule. This rule accommodates movement with four legs.
A "Trained Dancer" as the leader, can successfully lead an untrained lady around the dance floor because the leader is creating an environment that allows the lady to move naturally. It is much more difficult for a trained lady to follow an untrained leader. Basically the lady can dance only as well as the leader leads. The ideal situation is for the man and lady to both be "Trained Dancers" and understand the four-legged rules. I always tell the ladies: "Don't apologize for not being able to follow; if the man doesn't lead you can't follow".
The man creates and initiates the movement. The lady responds by feeling what the leader has created and responds accordingly. If the lady tries to figure out what to do she is already too late to respond to the lead. She must feel what to do and respond intuitively. At the higher levels of dancing, the lady doesn't just respond, she enhances, powers, and embellishes the lead.
The "Trained Dancer" as the leader, keeps his weight on one foot at a time so the lady can feel which foot to be on. The leader must power (move) from the supporting leg so the lady can feel the power and direction of the movement. New dancers often try to move from the free leg and consequently the lady has to try to guess what to do. There are "invisible" connections that are logical not physical as well. There is not just one lead. There are many depending on what you are trying to accomplish. The leader has to know how he wants the lady to respond.
The "Trained Dancer" as the follower, keeps her shoulders parallel to the leader unless he over rides this position. The leader can change the angle of his shoulders to create a shape that allows the ladies legs to cross in front or behind her depending on the shape of the shoulders and the direction of movement. This is just one instance of how the lady responds to the lead. The leader must know what he wants the lady to do. The leader dances the ladies every foot step.
Group Lessons are not intended to teach leading/following. Some Group Classes may mention it, but the primary goal is to teach the mechanics and the sequence of the individual's movements. Group Classes create what I call "Pattern Dancers". "Pattern Dancers" basically walk through pattern sequences with a partner that is learned in Group Classes as opposed to actually leading and following them.
The "Trained Dancer" is fundamentally all about "FEELING". The leader creates the feelings and the follower recognizes and responds to the feelings. This can only be learned with hands on by a trained Ballroom Dance instructor. "Trained Dancers" are developed in Private Lessons. The leader needs to learn to create the physical action that develops the feeling for the lady so she can respond in the correct manner. The lady has to learn how to respond to the feeling created by the leader. Since most men learn dancing mechanically and most ladies learn dancing by feeling, it looks like "they" got it right when it was decided who leads.