Chemical energy.

Potential energy stored within the structural arrangement of atoms within chemicals just waiting to be released via a chemical reaction. In this instance, a chemical reaction resulting in a very rapid burning of smokeless powder resulting in large amounts of hot gases being produced in a short time frame within a confined space. With nowhere for the hot gases to go initially the heat is not dissipated and so the rise in temperature accelerates the burning rate of the powder. With the expansion of the gases becoming exponentially quicker something has to give way and so the projectile is pushed out of it's brass shell and down the barrel of a firearm. A portion of this energy is converted to kinetic energy in the form of a speeding bullet. However this process is relatively inefficient since something like 30% of the total energy released is converted into kinetic energy of the projectile and the rest is lost as heat, kinetic energy to the gas and friction.