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.
An equation is balanced when both sides of the equation are equal to each other, hence making the equals sign in-between accurate. You must keep an equation balanced because, if you do not, the sides are not equal and your equal sign is false, leading your whole equation to be false.
