In E&M, one of the circuits we try to understand is a multi-loop resistor circuit. This is a circuit that has multiple batteries arranged in a way that takes away our ability to find the total resistance in the circuit. Basically, the multiple batteries ruin pure parallel combinations of resistors in our circuit. We cannot find the total resistance, and therefore cannot find a total current for the circuit. We need a new method since the traditional, usual method we learn to do does not work.
The technique of this video involves using Ohm's law and Kirchhoff's series rule (i.e. voltage of the batteries = sum of the voltage losses of the components of the loop) to set up loop equations, and then solve the loop equations for the loop currents. The math is algebra, specifically solving a system of equations for multiple unknown currents. Check it out, and I hope the example helps.