Basically, you are crunching an awful lot of numbers to get bitcoins as a reward in return. But since it is digital you'll need some mechanism so that people just don't copy a set of Bitcoins and then try to spend it all over again. After all, double spending is a characteristic of digital currency. This is where the whole proof-of-work function comes into the picture. Bitcoin uses the hashcash proof-of-work function as the backbone of it's mining algorithm. Every mining software that is working endlessly is trying to create a proof-of-work which makes their work unique and thus entitles them to a set of coins. So basically, Bitcoin uses an algorithm called hashcash to generate proof-of-work. It is costly in terms of time and energy consumed to produce for the pre-defined parameters. But at the same time it shouldn't require as much time to verify a proof-of-work as it takes to produce it. This is why the entire process revolves scanning for a value that when it is hashed two times with the SHA-256 hashing algorithm, the resulting hash begins with a pre-defined number of zero bits. The average effort need to hash such numbers increases exponentially with an increase in the number of zero bits required. This same generated hash however,can be easily verified by rehashing the number with a single pass of the double SHA-256 algorithm. So it is easy to verify but difficult to generate.
Then a simple question arises, if it was difficult to create for one machine then maybe two can do the job better. This is undoubtedly true, adding adding more hardware to the mix will give you more Bitcoins but only for a short while. When you increase the number of zero bits you increase the difficulty. And the Bitcoin network has its difficulty parameter readjusted every two weeks so that as time passes and more powerful computers join the network, the rate of creation is kept static. So the more popular it gets, the harder it becomes to generate Bitcoins. So much that normal computers can no longer generate Bitcoins at a profit. The amount spent for the electricity will far outweigh the value of the generated Bitcoins. yet people continue to mine. This is because of the specialised hardware that has been released which can generate Bitcoins at a pace far greater than ever before but while consuming far lesser amount of electricity.
Whenever anyone generates a proof-of-work it becomes part of the blockchain. The blockchain then serves as a ledger for every transaction that ever takes place. This is why all your transactions in the Bitcoin ecosystem can be traced from the very origin. Only after verification is the Bitcoin transaction happen. So if anyone would've programmed a Bitcoin wallet to show a balance of Bitcoins that never existed it couldn't ever be used. This is called the double spending problem and the concept of Bitcoins was conceived in order to solve the double spending problem. Whenever digital currency is generated, there is the possibility of copying that currency. And thus creating a duplicate which can be used like the original currency. Bitcoin does not have this issue thanks to the blockchain. Any person trying to scam the system needs to rewrite a good portion of the blockchain and that can only be done via a consensus. That is, a majority of clients hosting the blockchain must be convinced that a new addition /modification is infact been seen by a majority of clients. Unless this happens the new addition/modification is rejected. So it would take a few of the world's fastest supercomputers to actually change the balance of the Bitcoin economy. All of this makes the Bitcoin system very difficult to scam.
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