what is the importance of step four as man in relation to the next step to be taken and the lady for the reverse turn

Is it that the man steps backward and the lady forward?

Yes can you tell me why is that step is important for the man to do correctly in this figure.

The man is stepping backwards on 4, but the character of the movement requires that he retains control. The THT footwork (with the heel only 'just' coming into contact with the floor) before rising back to the toe to step to another toe on 5 allows this control, and slows the man's flight down, to make it easier for the lady to now turn around him. In particular, having made a proper inside turn action between 4 & 5 (with a pointing alignment of LF), the man waits for the lady to come around, before slipping the RF OP in CBMP, leaving the body underturned, before stepping again (typically into a Three Step) with CBM.

Carol. Please write your answer then I may be able to sleep.

LOL.........