What is milliwatt-hours?

A Milliwatt-hour is a unit of energy and its units, kWh, are formed with W for watt and h for hour from SI unit system combined with letter m, metric prefix, for 0.001 or $10^{-3}$. Its definition, in the context of electricity, is the energy of one watt power flowing for one hour.

Followings equivalent equations are identical but in different units. Please note that factor $10^{-3}$ is representing Milli prefix in mWh unit.

$$1 mWh = 10^{-3}*Pt = 10^{-3}*IVt = 3600 * 10^{-3}*J = 2.247 * 10^{22} * 10^{-3} eV = 8.598*10^5 * 10^{-3} cal$$

$P - Power$
$t - Time \text{ (in hours. Multiply by 3600 to convert to seconds)}$
$I - Current$ $V - Volts$
$J - Joules$
$eV - Electronvolt$
$cal - Calories$

Wikipedia page for Kilowatt-hour (watt-hour redirected to kWh) UCI article on Energy Units and Conversions Ian Woofenden's explanation on difference between Watts and Watt-Hours

What is Joules?

Joules measures energy. It is part of SI units system. Symbol for inches is $J$.

A Joule is commonly defined as amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied.

$$1\ J = 1\ kg*m^2/s^{2} = 1\ N*m$$

$$1\ J = 1\ Pa*m^3 = 1\ W*s = 1\ C*V$$

Where $J$ - joule
$kg$ - kilogram
$m$ - metre
$s$ - second
$N$ - newton
$Pa$ - pascal
$W$ - watt
$C$ - coulomb
$V$ - volt

Wiki page for Joules