Junction Rule
A junction in a circuit is a place where three or more wires come together at a point. Currents obey their conservation law at junctions the same as everywhere else:
This is sometimes referred to as Kirchhoff's junction rule. It is an important principle when we want to "solve circuits", by which we mean to find the values of the currents in the circuit, given the emfs of batteries and the resistances of any resistors. The currents serve as the unknown, and so the first step in "solving a circuit" is to identify how many unknowns there are.
Junctions are the secret to figuring this out, because they are the only place where a current can change: otherwise, when a current goes through a wire or a battery or a resistor, the current remains constant, because the current has nowhere else to go. Only at a junction does it have choices.
To find the currents in a circuit, then, we look at each junction, one at a time, and then for each junction we look at each wire. If the current in that wire has not already been assigned a variable name, then we name that current and also specify the direction* that the current goes. We then write a "junction rule equation" by adding up the currents that flow into the junction, add up the currents that flow out, and setting the two sums equal to each other.
Suppose we want to solve this circuit, which has four junctions.
For the first junction, we label all three wires as $I_A$, $I_B$, and $I_C$, and guess at the directions they will flow. We write a junction rule equation $$I_A=I_B+I_C$$
For the second junction, one of the wires ($I_C$) is already labelled, so we add two more labels, $I_D$ and $I_E$. We write the equation $$I_C=I_D+I_E$$
For the third junction, $I_D$ and $I_E$ are already labelled, so we only add one more label, $I_F$. We write $$I_D+I_E=I_F$$ The last junction has no new wires. We could write the equation $I_B+I_F=I_A$, but it turns out that this is redundant with the other three, and so we skip it.