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Let me take a stab at an explication. Full disclosure, I do mine crypto currencies and I have patents in encryption.

Some basics first-
“Currency” is something that REPRESENTS value but does not of itself, have value. The US dollar is a currency. While it can be exchanged for goods and services, the ink and paper of a dollar bill is of little use. This differs from “money”. Money has value such a gold and silver. Even certificates of gold and silver are considered money. While the terms are often used interchangeably, they are in fact, not. The US left the use of money behind when the dollar was removed from the gold standard at which time it became a currency.

There are more challenges with creating currency that money. Since a gold coin would require ... gold, there is a limit to the money supply via gold coin. With currency, counterfeiting is a significant problem that must be prevented. Since the dollar is paper and ink, significant efforts have been made by the US Treasury to make the dollar unique (I wont go into all the details) and laws have been established to make counterfeiting illegal. Understand that crypto currencies do not have the benefit of those laws so some other means must be used. This is to prevent just anyone from creating all the bitcoins the want. So bitcoin, not having the protection of counterfeiting laws, has to create STRUCTURAL limits. This is done by using a “hash” algorithm.

Side discussion about hashes.
Hashes are one way cryptographic functions. The intent is to make it extremely difficult for the original to be changed without detection. Think of a word document. Without protection, any one can edit the document and represent it as the original work. However, if you generate a hash of the document after it is created, then you can detect that the document has changed by comparing the original hash to the new document hash. If the hashes are different, the documents are not the same. HOWEVER, if the hashes ARE the same, it is the same document. This provides the basis for blockchain. A series of transactions are recorded in a block, the block is then hashed and that hash starts the next block (next link in the chain). Thus if anyone tampers with one of the transactions - by so much as 1 bit - then the hash is no longer valid and the chain is broken. Anyone who checks the hash values can detect the broken chain.

Now as to specific “mining”
So what is needed is a computer algorithm that is large/complex so that it requires extensive sets of computer solving in order to be valid. As an example, think of the old checksums that we used to run on downloaded files. If any checksum would work, then it could be repeated by anyone else and somewhere down the road, a computer would be fast enough to create a hash (checksum) fast enough to defeat the ability for the network to validate a transaction. So the problem has to be “larger” than just executing a single hash algorithm. So now lets introduce some variables

S = source
P = pad
O = outcome

In overly simplified terms, the puzzle that has to be solved is as follows:

The hash(S) + P must equal a specific O

Assume that the specific outcome must start with four bytes of all ones (0xffff....). In order to solve the above equation and since hashes are only one way operations (they can not be mathematically reversed or solved backwards), the only way to solve the above is to try a series of pads and keep checking the iterations of pad until you have found a pad that works. This is a brute force method and is very computer intensive.

This is what a miner is doing. They find the next working pad and that correlates to the next coin.

This is a grossly oversimplified description and more information can be found at: https://www.investopedia.com/terms/b/bitcoin-mining.asp