"I don't understand the pressure: who is applying it the gentleman or the lady?"
Pressure by physical definition must be mutual. The light pressure between the man's right hand and the lady's left back has to be applied equally by both. If it's not, the hold would be expanding or contracting until it is.
Something that's not often realized, but often encountered, is that less experienced couples in which neither partner comes with built-in padding, will find it hard to have a good connection at both the lady's left back and between their chests. It takes a lot of experience for a lady to learn how to fill up the space between the man's ribcage and a reasonable position of his wrist, without distorting her posture.
As a result, to learn the left back/right wrist part of the connection, it can be useful to spend a substantial period of time intentionally dancing with a slight space between the bodies. This will tend to develop both dancers' sense of balance over their own feet, and their perception of the partner through their frame. Only later, once that is set, will it be possible to dance in contact with sound technique and while maintaining a functional frame - try to do it all too soon, and many parts will suffer.