Madison Teachers, Inc. Solidarity enewsletter via a kind Linda Doeseckle email (PDF):

When a union member files a grievance it means that the member and his or her union believe the employer has failed to live up to its end of the Collective Bargaining Agreement. They are called “agreements” for a reason: the union and the employer have agreed that what has been agreed upon in negotiations is what both parties will live by, that it is best for the employee and the employer. A Collective Bargaining Agreement is a legally binding Contract.
Filing a grievance sets in motion a process for resolving the employee’s complaint. Once a grievance is filed, the union and the employer meet in a process set forth in the Collective Bargaining Agreement to discuss the reasons it was filed. When the issue cannot be resolved through discussions, the union may take the complaint to a neutral third party (an arbitrator) who will decide whether the Contract has been violated. Wisconsin law assures that union- represented employees cannot be retaliated against because of filing a grievance.
The Collective Bargaining Agreement is the Constitution of the workplace, and only unionized employees, like members of MTI, are protected by a Collective Bargaining Agreement.