First thought

In some ways, Bitcoin mining is like mining gold. There is a limited amount of bitcoins, similar to gold, and the more you take out, the more difficult and resource-consuming it is to find. The major difference is that no one swings a pickaxe to get bitcoins. In fact, miners are getting rewarded for resolving complex mathematical problems. But how?

The more you get into it, the more complicated it becomes

First of all, mining requires the necessary equipment to do this. The miner needs at least a computer with the vast computing power available. Nowadays our personal computers can not handle the mining, which is simplifying speaking ultra-fast number guessing. Competition is so fierce, that entrepreneurs started to manufacture dedicated units just for solving bitcoin game. The Bitcoin algorithm adjusts the difficulty of chance for a win, parallelly to the amount of computing power in the network. The winner is a first miner, who announce the correct result. This is called the Proof of Work function. As a reward of this effort, the system allows a miner to add a transaction of 6.25 BTC to any wallet. This is how new bitcoins are distributed.

Want some more?

Bitcoin miners do not only mine.

They verify transactions or avoid the so-called double-spending

Bitcoin miners need to store all transactions captured in one database(blockchain). This mechanism proofs that someone spending the bitcoins is a legitimate owner and also prevents double-counting or any other type of cheating.

If it is still not enough...

The whole process is obviously more complex as you may guess, what brings a potential risk for users, caused by frauds and attackers. Fortunately, the Bitcoin blockchain is the oldest, most developed, and supported by the biggest community, what makes it bulletproof nowadays.

Do not be scared, just read about famous 51% attacks on so called 'weak/cheap' blockchains here.