Kirchhoff's current law, states that the total current flowing into the junction in an electrical circuit, must be equal to the total current flowing
(A junction in an electrical circuit, is where several conductors are joined together.)
Kirchhoff's current law, is an example of the law of conservation of charge, applied to a junction in an electrical circuit.
Conservation of charge states that charge cannot be created or destroyed. As current is just the rate of flow of electrical charge, then if the current flowing into a junction was not equal to the current flowing out, this would mean that charge was either being lost or gained at the junction! This would violate the law of conservation of charge!
(A junction in a circuit is also called a node.)
Kirchhoff's current law can be used to find an unknown current, flowing into or out of a junction, if the magnitude and direction, of all the other currents at the junction are known