Bitcoin is like an open book to all in digital format, with the registration of all balances of each bitcoin address, actually, with the record of all transactions between bitcoin addresses in chronological order. All that help keep this book's transactions and balances are called "miners" - in analogy to the exploration of gold - and actually nothing is created, crafted or minted but you may happen to get a few slices of a huge "digital pizza" with a limit of twenty-one million slices, as a reward for verifying transactions and keep the book open to all and reliable on on a distributed computer network - that is, without a central point of failure.
These rewards - or pizza slices - are called bitcoin coins but note that they actually exist only as balances associated with a bitcoin address and corresponding private key.
What is kept private is these private keys of each bitcoin address and this information is stored in a special file called a wallet (walltet.dat) that protects this information making it invisible and hermetic as much as possible.
The work of the mining computers is to make transactions become irreversible, using trial and error until they find a place in the chain of blocks which make them irreversible. The difficulty level of this trial and error to find a place in the so called blockchain is the scheme that makes transactions irreversible and avoids double-spending from bitcoins from these addresses in the chain of transactions, and it is adjusted every two weeks, so that a new block is inserted every ten minutes - no matter the amount of computational power of the network -, with corresponding reward of pizza slices, not coins, to "miners" that actually created the last block to be added - usually collaborating in pools with other miners in order to have more chances of not missing the reward. They receive the pizza slices, not coins
to the bitcoin address they designate for that purpose.
This reward is called coinbase and is what makes the value of bitcoin coins for circulation. Yes they are coins, not slices of pizza. But if you want to think it with slices of pizza, you can happily say that actually there are no coins: simply the "miners" receive slices of pizza in their designated bitcoin addresses, thus allowing transactions between bitcoin addresses.
The numbers used by the mysterious Big Daddy of bitcoin, Satoshi Nakamoto, are somewhat arbitrary and empiric but work well and seem to have been inspired by gold mining anologies, as well as to provide a reasonable monetary mass, that could become comparable to the U.S. dollar by 2030.
The private key and bitcoin address form a pair and are like a key and a locker, or as a password and your bank account. But their mathematical properties are very particular because it is possible to calculate in some fractions of a second the bitcoin address, in a pair, from its private key. But the reverse would take countless millions, if not billions of years as it would have to be done by trial and error, even if quantum computers were used.
It is possible to think that with a lot of luck you could find a private key and generate a pair so that the corresponding bitcoin address had balance worth stealing but the probability of this happening is certainly much less than three lightnings falling upon the same person and him remaining alive, though that may have already happened in the past.
To decrease the risk you must have many bitcoin addresses in your walet. Having the bitcoins well distributed in our(s) wallet(s) ensures it will be much less likely there will be a chance of seeing all your bitcoins disappear magically.
If you encrypt your wallet and have the bitcoins distributed in many addresses, you must be safe.
[EDIT]
The limit of 21 million bitcoins results from the accumulation of 50 bitcoins reward each ten minutes during the first four years(50x6x24x365x4=10 512 000), plus, half, 25 bitcoins reward each ten minutes during the following four years (5256 000+10 512 000= 15 768 000), plus, half, 12.5 bitcoins reward each ten minutes during the following four years (2 628 000+5 256 000+10 512 000=18 396 000)... and so on and so forth, till the reward of the fours years before is so that it doesn't add nothing to the total of "almost" 21 million, more precisely: 20999999.97690000 BTC.
Here is the code that imposes this limitation,
//on main.cpp
int64 static GetBlockValue(int nHeight, int64 nFees)
{
int64 nSubsidy = 50 * COIN;
// Subsidy is cut in half every 210000 blocks, which will occur approximately every 4 years
nSubsidy >>= (nHeight / 210000);
return nSubsidy + nFees;
}
