The algorithm relating to bitcoin minning is a some kind of Encryption/decryption process, which is called SHA-256 hasing algorithm. That's why the mining and hashing are sometimes both used interchangable.

SHA-256 hashing is a quite hard process, which means it could be only sovled by brutal force, e.g. using computer calculation to search every possible answers to find a real solution. But don't think you can solve one definite problem using your own computer, which nowadays is not possible. Becausing during your hashing process, there are other T hasing/s computers calculating the same problem and once the problem is solved, the problem itself will be updated accordingly. This kind of design determines that the most amount of hashing power you have, the quickest solver you will be, and you can mine most bitcoins.

However, the difficulty of the problem itself, is dynamically adjusted by the network, which is adjusted according to the total hashing power on the network, so that every 10 minutes on average, a block can be generated. The return of a block, nowadays, is 25 bitcoins. After some years(4 maybe), the return will be further reduced by half. Finally, there will be no returns of generating a new block, but only transaction fees. So the total amount of bitcoins will be 21 milion and will be changed forever. All this kind of rules have been coded to the bitcoin software so no single party can change it by itself, which means bitcoin network has no central bank, or some kind of currency issuing department.