Think of a narrow pipe (resistance) through which water flows (current); the friction generated by the water rubbing against the pipe walls heats up the pipe, similar to how electrical resistance causes heating in a wire.

P-I-R: 'Power is I-squared R' (or simply think of 'Power-squared R' for current).

According to Joule's law, when an electric current $I$ flows through a conductor with resistance $R$, the work done to push the charge against the resistance is converted into thermal energy. Power is the time rate of doing this work. Since the potential difference $V$ across the resistor is given by Ohm's Law as $V = IR$, substituting this into the general power formula $P = VI$ yields $P = (IR) \times I = I^2 R$.

Remember that $P = I^2 R$ is best for series circuits (constant current), while $P = \frac{V^2}{R}$ is more useful for parallel circuits (constant voltage).