Kirchhoff's laws: current is conserved and voltage sums to zero round a loop

All the current that comes in goes out, and going once round a loop the voltages sum to zero. The starting point of all circuit analysis.

Current law (KCL)

All the current that enters a point leaves it.

The sum of currents into a point (node) = the sum of currents out. Charge does not pile up or vanish.

Example: 100 mA comes in from the supply, 20 mA leaves towards the LED and 80 mA towards the MCU.

Voltage law (KVL)

Round one loop, the voltage gained and the voltage dropped sum to 0.

Add up the voltage rises and drops once round a closed loop and you get 0.

Example: 5 V supply → resistor (2 V drop) → LED (3 V drop) → ground. 5 - 2 - 3 = 0.

Where it is used in embedded work

Power budget: adding up every load current on the board to size the regulator is KCL.
Checking voltage drops: subtracting all the drops across long wires, connectors, fuses and reverse-polarity diodes, and checking that the chip still gets its minimum operating voltage, is KVL.
Debugging: if the voltages you measured do not satisfy KVL, either the measurement is wrong or the real board differs from the schematic.

Add Ohm's law to the two laws and every resistor circuit can be solved as simultaneous equations. The divider rule and the Thevenin equivalent in the next steps are shortcuts for this calculation.