Right a quick lesson in terms and mods..
Induction - Air filter basicaly, OEM is normallt restrictive, so people change them for better flowing pieces of kit.
Mani/Manifold/Header - The four tube thing that comes off the back of the engine and feeds the gases out of the cylinder head and into the exhaust. General rule the bigger the tubes the better/faster the gases can escape.
Cat - Catalitic converter, filters most of the nasty crap out of the gases, can be restrictive, race cars dont have cat's so that the gases get out quicker. De-Cat.
B-pipe/Centre pipe - The piece of exhaust that stretches from the cat to the back box, again, the bigger the bore the more gases can get down there better.
Back box - Your triangles surrond the end of this, pretty much makes the final sound of your exhaust system, OEM can be restrictve so after market ones are generaly better, again, you guessed it gets the gases out quicker.
The running theme here is getting air in quicker and gases out quicker. The quicker you can get the gases out the quicker you can get air in and therefore get more power.
Mapping/ECU/Fueling/KPro/K100 - These are basically all comoputers for you car, that tell it when to inject the fuel into the cylinder chamer for burning and creating power. Increasing the air flow through the engine is good for starters but further down the line can damagae the engine by messing with the air fuel ratio. These new computer 'maps' alter the fueling to compenstae for the better air flow, resulting in, more power. This is normally the last thing you do to a car, like the icing on the cake, gets all of the mods working together better.
Thats the basics.
Sorry if im teaching you to suck eggs.
Hope this helps.