Some of the prophet's wives vied with one another, on dividing the prophet's leisure and spare time; and caused some difficulties for the prophet through their disputes. Although the Messenger of God strictly observed the rules of equality and justice with them, yet their disputes still continued. The above verse revealed giving him the necessary authority on account of his leisure and spare time, which was rare, in order to do what was rightful.
To put this in another way, we may say:-
A Moslem cannot have more than one wife if he is not apt to treat his multiple wives justly. This is because in Moslem household, there is no room for a physically favourite wife.
Our prophet in his special position was forced to hold several wives, and he did his best to observe the rules of justice and equality with them all, particularly in the matrimonial relations. But for a man in his position it was not so easy to observe equality in the rotation of the wives, and their reception and rejection. In any case the prophet ignored all his personal considerations.
So the above verse sets the prophet free from some obligations on account of the turns and being in seclusion with one of his wives.
By some exchange of rotation, the prophet through the above verse, could manage to cheer up and cool the eyes of those who had missed their turns and could have been disappointed.