Kirchhoff's Current Law explained?

what goes in must come out.

If you have encountered Kirchoff's law(s), then you have a text book that should explain it and have examples.
Read it

Kirchoff's laws are really just basic common sense.

The current law says that the sum of currents entering a node equals the sum of currents leaving the node. All that really says is that it is impossible to have current build up (or disappear) at any place in a circuit.

The voltage law says that the sum of voltages around any loop in a circuit must equal zero. You have to be very careful with the sign of your voltages here. But again, if you think about any loop in a circuit, if you start at any point and go around the loop adding up the voltages that you encounter, then by the time you get back to where you started, the voltage must be the same* so, obviously, the sum around the circuit must be zero (The voltage at point a is Va. The voltage at point a, including all of the other voltages in the loop is also Va. Va = Va + all_voltages_in_loop. Therefore all_voltages_in_loop = 0).


*all of this stuff assumes that the circuit is in a static state or that you are looking at a snapshot of the circuit at a specific time

Kirchhoff's Current Law, also known as Kirchhoff's Junction Law and Kirchhoff's First Law, defines the way that electrical current is distributed when it crosses through a junction - a point where three or more conductors meet. Specifically, the law states that:
The algebraic sum of current into any junction is zero.
Since current is the flow of electrons through a conductor, it cannot build up at a junction, meaning that current is conserved: what comes in must come out. When performing calculations, current flowing into and out of the junction typically have opposite signs. This allows Kirchhoff's Current Law to be restated as:
The sum of current into a junction equals the sum of current out of the junction.