What would happen if mass were not conserved?

In most cases, it is impossible to have a reaction in which mass is not conserved.  However, nuclear reactions sometimes start out with more mass than they end with due to the fact that some of the mass is turned into energy.  This is why E=mc² is so important, it relates energy to mass.  In a nuclear reaction, if some of the mass is turned into energy, a huge amount of energy is released.
I hope this helps.

The flowers in a flower arrangement are actually alive