This is a phrase used in baseball to refer to a manager who identifies very closely with the needs of their players. Typically, the manager is a former player themselves, though this is not always the case. This type of manager provides a powerful voice in the organization and makes sure the views of the players are understood. A players' manager is usually a lot closer to their players, and reinforces it by engaging the players professionally, socially, and any way they can.
A players' manager is not the style of every manager, including those who used to play. This style of managing involves being on the players' level, rather than at an elevated level in the team structure. Depending on the team and the manager, this may or may not lead to a winning season. It is important that players' managers are matched with the right team; otherwise the results may be less than optimal.