youll certainly get a better technical explanation, but in plain English, a cars moving parts (pistons, gears etc.) are designed within certain tolerances. On most mass produced cars these tolerances are wide and can explain performance variations between one car and the next off the assembly line. By running in a new car/engine, you will cause the various components such as pistons to adapt to the cylinder bores and form a better seal. You will also avoid damaging the gear cogs in your gearbox, etc etc. That in turn leads to better performance, or I should correct that it leads to not losing performance. A good example is that ragging the car from day one and when its cold etc may cause improper seals between pistons/cylinder walls leading to eventual combustion gases (blowby) escaping past the piston rings into the cranckase and doing bad stuff down there etc.
Running in should be done properly at different rev ranges without unecessarily loading the engine etc. same with gears.
HTH