what does check and balance mean or a check and balance system, or checks and balances?
Not a teacher.
It means that there are independent organizations that have different powers that are used to keep the other organizations in line. The easiest example I can think of is the American system of government (ideally anyway).
The Executive (president) can veto bills passed by Congress, but can't actually present any bills of his own. Members of his party need to present bills that he wants enacted. The President is also Commander in Chief for all the US Armed Forces, and the chief diplomat.
The Legislative (Congress) has power over taxes, introducing legislation, enacting treaties, and declaring war.
The Judicial (Supreme Court of the United States) can declare the actions of either the Legislative or Executive unconstitutional, that is, against the Constitution of the United States. The President appoints new justices, and the Legislative has to approve them.
Each of the branches of our government should be able to keep the others under control (in check) through their assigned powers to keep a balance of power. The same systems can be found in companies and other organizations. For example, few companies allow their executives exclusive control over the company's finances. There is also often a Board of Directors who can override the executives' decisions.