Kirchhoff's current law:
Currents that flow into a node are positive, currents that flow out of the node are negative, and their sum is zero.
The principle that stipulates KCL: the law of conservation of charge.
Kirchhoff's voltage law:
The sum of voltage drops on elements along a loop of given direction equals the sum of voltage s of power supplies. Currents flowing in the direction of the loop cause positive voltage drops, likewise, voltage sources with higher potential in the direction of the loop are also positive.
KVL is based on a principle of conservation of energy.
If the solution of a circuit gives us negative value of a current, it means that this current (of positive value) flows in opposite direction.