The main components of power board of laptops

Wikipedia is your friend
http://en.wikipedia.org/wiki/Capacitor
http://en.wikipedia.org/wiki/MOSFET
http://en.wikipedia.org/wiki/Diode

Capacitors store energy tand also filter out high frequency noise, MOSFETs(Transistors) are switches, depending on their configuration you can use them in combination with capacitors, inductors, diodes and transformers to increase or decrease the voltage.
Diodes are one way valves for electricity.

If you want to learn more about how a power supply or power board in a laptop works there is a nice article by crmaris at TechPowerUp, power supplies and power boards do about the same thing, the power board is just the secondary side while the primary side is in the power brick for the laptop.
http://www.techpowerup.com/articles/overclocking/psu/160