Power is the rate of transfer/conversion of energy. Due to energy being the ability to do work, power can also be defined as the work done per unit time: $$ \begin{equation}\begin{aligned} P=\frac{E}{t}\\ \end{aligned}\end{equation} $$
The SI unit is the Watt ($W$), equivalent to a Joule per second: $$ \begin{equation}\begin{aligned} P&=\frac{E}{t}\\ &\rightarrow \frac{J}{s}\\ &=W\\ \end{aligned}\end{equation} $$
The kilowatt-hour
Because energy is the product of power and time, the kilowatt-hour is a unit of energy: $$ \begin{equation}\begin{aligned} E&=Pt\\ &=1 kW\times h\\ 1kWh&=1000 W\times 3600 s\\ &=3,600,000 J\\ &=3.6MJ\\ \end{aligned}\end{equation} $$
Electric utility companies often charge a fixed rate per kilowatt-hour. This is why tech companies that provide hosting services locate their servers in places where the rate per kilowatt-hour is low. Operational costs are lowered because of lower rates, thus making the hosting business model more sustainable and profitable.
Efficiency
This is the percentage ratio of the energy output of a system/machine to the energy input: $$ \begin{equation}\begin{aligned} \text{efficiency}&=\frac{E_{out}}{E_{in}}\times 100\%\\ \end{aligned}\end{equation} $$
Energy when used becomes work: $$ \begin{equation}\begin{aligned} \text{efficiency}&=\frac{{\text{work}}_{out}}{{\text{work}}_{in}}\times 100\%\\ \end{aligned}\end{equation} $$
Considering a fixed time interval measuring these two values, we can also expressed efficiency as the ratio of the powers: $$ \begin{equation}\begin{aligned} \text{efficiency}&=\frac{P_{out}}{P_{in}}\times 100\%\\ \end{aligned}\end{equation} $$
Power and velocity
We know that energy/work is the dot product of the force and the displacement of the object: $$ \begin{equation}\begin{aligned} E&=F\cdot s\\ \end{aligned}\end{equation} $$ If we divide both sides by time we get: $$ \begin{equation}\begin{aligned} \frac{E}{t}&=F\cdot \frac{s}{t}\\ \therefore P&=Fv\\ \end{aligned}\end{equation} $$
Power is the dot product of force and the velocity of the object.