Madison Teachers, Inc. Solidarity Newsletter via a kind Jeanie Kamholtz email (PDF):

When a union member files a grievance it means that the member and his/her union believes that their employer has failed to live up to its end of a provision which the employer agreed to include in the Collective Bargaining Agreement. They are called “agreements” for a reason: the union and the employer pledged that what they agreed upon in negotiations is what both will live by, that it is best for the employees 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, often a complaint which could have been resolved easily and informally through discussion. 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 on which the grievance is based. 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 management has violated the Contract. 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.