The blockchain network is legitimized by miners. Different currencies use different algorithms, Bitcoin’s algorithm being SHA-256. Miners use their computer hardware (GPUs or ASICs) to rapidly guess and check solutions to the algorithm. It’s so difficult that it’d be next to impossible for humans to solve it.
The faster the GPU can guess and check solutions, the more likely it is to successfully solve the problem. When this happens, a block reward is received. This means the miner who successfully solves the block receives 12.5 Bitcoins directly deposited into their mining wallet.
It takes about 10 minutes for miners to verify one block. Every time a block is added to the blockchain, the previous layer is sealed off. This ensures the same person can’t send the same Bitcoin twice.
There are only 21 million Bitcoins that can exist, and currently about 16 million have been mined. Every 210,000 blocks, the block reward splits in half. When Bitcoin first came out, the block reward was 50 Bitcoins. 210,000 blocks later it became 25 Bitcoins, and now it’s 12.5 Bitcoins.
As the block reward halves, theoretically, the price of Bitcoin (or whatever currency you’re mining) should increase accordingly. Once all Bitcoin are mined, the price should be much higher. At this point in time, miners will receive rewards in the form of transaction fees which are deducted from every transaction.