In order to balance an equation you must have equal numbers of atoms on either side.
eg) H2 + O2 => H2O
On one side we have 2 hydrogens and 2 oxygens, while on the other side we have 2 hydrogens and one oxygen. If we multiply the H2 and the H2O by the coefficient* 2 maybe we will end up with the right amount of atoms.
eg) 2H2 + O2 => 2H2O
Now we have 4 hydrogens and 2 oxygens on one side, and 4 hydrogens and 2 oxygens on the other. We are balanced.