In the Mass Effect universe, there used to be limited need for ammo, since it was explained that each weapon used a large block of metal from which it would actively 'shave' off tiny pieces to use as bullets. Then, in the second Mass Effect video game, apparently guns got more powerful and therefore generated more heat. So they added the ability to replace heat sinks to keep firing the gun. Each heat sink had a limited number of shots before it expired.
The 'shaved' bullet is fired by using eezo (electrical current, positive or negative, can change the mass of an object) to reduce its mass so it can be easily accelerated to a high speed.
Since a weapon has to actively make its own bullets, charge the eezo chemical to reduce bullet mass, and propel the bullet, it is generating so much heat that the newer weapons need heat sink replacements regularly during combat (heat sinks were limited to maybe 20 or 30 shots per sink).
What is generating all of this power? Modern day weapons use explosives. But in the Mass Effect world that wouldn't be able to account for all that the weapons are supposed to do. How are these handheld weapons powered?