What do the coefficients located before certain molecules in each chemical equation represent?

It represents the number of moles required of that molecule to balance the chemical equation, which means to have the reaction chemically happen and goes to completion.

For example:
CH4 + O2 --> H2O + CO2     that is not balanced

with the coefficients located
CH4 + 2O2 --> 2H2O + CO2    now with the coefficients the number of oxygen and hydrogen on each side are equal