The current division rule is used to determine the current flowing through different branches of a parallel circuit. It states that the total current entering a parallel circuit will divide among the branches based on each branch's resistance. The current through each branch can be calculated using the current division rule formula, which relates the branch currents to the total current and the resistances of each branch. The current division rule is useful for circuit analysis and design, though it assumes resistances are purely resistive without stray capacitance or inductance effects.