Answer is: They tell us how many of the entire molecule to their right there are involved in the reaction.
For example we are going to use this unbalanced chemical reaction:
H₂ + O₂ → H₂O.
First, calculate number of atoms (hydrogens and oxygens) on left and right. There is two oxygen and two hydrogen on left and two hydrogen and one oxygen on right.
You can not change molecular formula of compound, only you can put coefficient in fron of compound to balance reaction.
Put 2 in front water to balance oxygen (now you have two oxygens on left and right). But now you have four hydrogens on right, so you must put 2 in fron hydrogen on the left.
2H₂ + O₂ → 2H₂O.