Tightening the rope
If you've ever watched a tug o' war competition, or taken part in one, one of the first instructions after picking up the rope is to take out the slack. Each team adds just enough tension to the rope to remove any slack and then from there the referee signals for the rope to be moved in one direction or the other so that "center" marking on the rope is centered over the corresponding mark on the ground.
Taking out the slack is a process of tightening the rope.
Working with milling machines (bearing in mind this was 20 or more years ago, technology may have changed), when moving the vice in one direction or the other, we first had to take out the slack. Once the slack was taken out, then we could finely control the movement of the vice relative to the machining tool.
Creating a connection
With a tug o' war, taking out the slack means that each team can directly feel the effort the other team is exerting via the rope. There is no delay. The rope, with slack taken out, transmits force between the opposing team. This force does work, but it also transmits information.
If one team feels itself being pulled towards the center line, they respond (or try to) by trying to exert more effort. Likewise for the other team.
Prior to the slack being taken out of the rope, the teams have no connection. If both teams pick up the rope, but the rope is still slack, then the weight of the rope will exert a pull of sorts, but still the teams have no means of "feeling" each other or affecting each other until the slack is taken out. Once the slack is removed, they can feel each other and affect each other.
Changing the intent of the game
The intent of the game, the tug o' war is what guides how they then use these inputs and outputs.
What if the game was to match force and to keep the rope centered? This would be equivalent to two people leaning against each others hands with arms forwards and slightly up. In order to stay balanced, teach person has to feel and modulate their applied effort. If one person begins to relax, they can then be pushed by the other person, so either both people have to relax together, or the person who was relaxing has to re-exert to re-establish balance.
Keeping the slack our requires effort
In all of the above cases, taking out the slack requires some sort of effort. And keeping the slack out requires continued effort.
Better than the sum of the parts
In social dance, in order for two people to dance well together, to become bigger and better than the sum of the parts, each person has to take out the slack in their own body, but also in the connection between them. The general term for how a person holds themselves in social dance is frame. A person with a good frame has a frame that is not too rigid but also not flaccid. When two people with good frames connect, they can dance well together.
Two sides of the same coin
For two people to dance well together, an important idea is that one person is the lead and the other is the follower.
For any relationship to work, (for any relationship to create change, or resist it) a stable foundation or anchor point is required. In dance, this anchor point is the person called "the lead". The lead isn't better than the follower. They are two aspects of the same thing, the dance. But these two roles are required if a couple wants to be able to dance well together.
In dance, the lead is the person who choses the move. He or she may also direct the dancers on the dance floor, looking for space to move into, or creating it so that the follow has room to execute.
The follower executes the move, expresses it.
At a very basic level of dance, the lead often acts as a still point or foundation around which or from which the follower executes a move. And rather than just signalling a move, a good lead continues to monitor the floor and their partner making any adjustments necessary so that the follower can execute easily and comfortably. Doing any sort of turn where one hand is held, the lead can adjust the position of their hands relative to themselves or their partner so that as the partner turns their wrist is comfortable.
Transmitting and receiving information instantaneously
With a good frame, i.e. one where the slack is removed, dancers can both feel each other, and affect each other. As the lead moves forwards, their forward move is transmitted via their arms (and or body) to their partners arms (and or body) and as a result the partner can move back as the lead moves forwards.
If slack is totally removed, then this transmission of intent is instantaneous and as a result the two can move as one.
As an aid, the lead may signal ahead of time via changes in hand position and hand pressure so that the follow is ready to move in the required direction.
With rehearsed sequences of movements, this pre-signaling may be less important.
With more experienced dancers who are tuned into to each other (and whose frames are rigid enough to remove slack but not so rigid that they lose sensitivity) the follower may be able to feel ahead of time what the lead is about to do without the hand signaling. In this case, any changes are transmitted from the center of the leads body via tension to the hands and the follower can feel those changes.
With dance, this kind of tension can be used so that two people can dance as one.
In martial arts the idea can be to try to control tension, by going slack in places, to mask intent.
Taking out the slack is a way of instantaneously transmitting and receiving information while at the same time also effecting, or trying to effect, a change.
Taking out the slack is a way of creating a relationship so that one part of the relationship affects the other and vice versa.
Taking out the slack requires effort. It also requires sensitivity. And it requires an understanding of what you are trying to do. And of course, it also takes practice.