When you talk about balanced equations you are talking about chemistry.
Chemical equation balance is to make sure that there are the same number of atoms of a given element in the right side than in the left side.
It is a chemical principle, the atoms do not create or destroy in a chemical reaction, then you have to count the same number of every kind of atoms in the left side than in the right side.
For example:H2 + O2 -> H2O is not balanced because there two atoms of oxygen in the left side and 1 atom of oxygen in the right side.
To balance this equation you have to insert coefficients:
2H2 + O2 -> 2H2O. Now you have 4 atoms of hydrogen in each side, and 2 atoms of oxygen in each side, making sure that none atoms was created or destroyed in the reaction.