To start it took 1000 calculations to reward a bitcoin, something easily achieved by one computer that was doing 100 calculations per second. However there were a few other computers/miners all mining the SAME bitcoin. After 999 calculations were made the computer that (by luck) mined the last bitcoin to complete tot 1000th calculation is awarded a bitcoin. When this bitcoin was mined the calculation became harder. This has been going on exponentially until now, and now many billions of calculations are needed to mine a single bitcoin. The more power your computer has, the more likely it is to be the one that makes the last calculation before the bitcoin is rewarded. Think of it like 100 diggers all digging for a single piece of gold. The one who strikes the gold gets it. The value is simply created by desire and rarity. It is again comparable to rare metals in that the more scarce they become the more value they have. There is no way for the government to know what you are doing (without a personal hack) with your money. You can buy drugs, or guns, or anything else, and other than the usual digital trail we all have when using the internet (that can be minimised or wiped out) there is no paper or digital trail.