turbo basically uses the exhaust gasses to spin the impeller wheel, which sucks in and compresses air and pretty much forces it into the engine, meaning you get more compression pretty much.
Intercoolers, basically they are a heat sink. You have your sort of solid rows in the middle which the compressed air goes through, and then you have like this see through mesh bit. The air passes through this, cooling the metal and the surrounds, including the compressed air. etc etc etc My brain hurts too much to explain any more atm
also check out http://www.prestigemotorsport.com.au/modules/turboTalk/
good info in there