All of this can be understood by two equations:
\$ E = IR \$
\$ P = IE \$
a combination of Ohm's law and Joule's law
To know how much heat/light/mechanical/chemical/whatever energy is being created as a consequence of the electrical energy being used, you need to know the voltage drop and current. The electrical power, as given by the product of voltage and current, is exactly the rate of energy conversion from electrical to something else.
If you consider what happens if you put an ideal short (zero resistance) across an ideal battery (perfect voltage source), you get a very different universe than the one we have. By Ohm's law, a short can't have a voltage drop:
\$ E = I\cdot0\Omega = 0A\$
But an ideal battery has always exactly the same, non-zero voltage drop. The contradiction means it's impossible. To consider why, think of what happens if you connect a resistor across a battery. As the resistor gets smaller, more current flows, and the power increases. As the resistance approaches \$0\Omega\$, power approaches \$\infty\$. Since we don't have infinite energy available to make infinite power, this can't happen.