Kirchoff's voltage and current laws basically state that voltage or current in a circuit must be accounted for - it cannot just 'disappear'. The laws are as follows:
Kirchoff's Current Law states that 'the algebraic sum of the current meeting at any point in a circuit is zero'.
I3 = I1 + I2
or I1 + I2 - I3 = 0 (currents towards point designated as positive, those away from point negative).
In other words the sum of all currents entering a junction must equal the sum of those leaving it.
Kirchoff's Voltage Law states that 'in travelling round any closed mesh (section) of a network (circuit) , the algebraic sum of the emfs (voltages) acting in the mesh is equal to the algebraic sum of the IR voltage drops for the individual resistance in the mesh.'
IR1 + IR2 = E1 - E2
-IR1 - IR2 = E2 - E1
In other words the sum of all voltage sources must equal the sum of all voltages dropped across resistances in the circuit, or part of circuit.