When we read article on mining, we get a term "solving mathematical puzzle". To get a block, miner needs to solve the mathematical puzzle and whoever can solve the puzzle will be able to get a block and thus the reward (I can be wrong technically, this is what I know).
What's this puzzle all about? What do miner exactly solve? Please try to avoid technical term if possible, I would like to know in easy way.
I will try to keep this simple.
To understand the puzzle you will first have to understand how the SHA256 algorithm works.
Each block contains a merkle root, block header, block size, transactions, transaction count, nonce etc...
A miner uses his hashing power to generate hash of a block. This is where the SHA256 hashing algorithm comes into picture.
Example:
https://www.blockchain.com/btc/block/0000000000000000000ab0825fc30cf2844723262e0c0f2bfd048b2e752029daThe mathematical puzzle which the bitcoin miners solve are nothing but the hash with required number of leading zeroes.
The number of leading zeroes are determined based on the difficulty and when a miner finds out the particular hash, it signals the other miners regarding the same thus claiming the block rewards.
You made it more complicated rather than making it simpler

It is also not about "leading zeros" but a very simple integer comparison where we want a to be smaller than or equal to b and for example 0035 is bigger than 0031 and is rejected even though both have 2 leading zeros.
A simple explanation of mining IMO would be to compare it with rolling a dice.
Imagine if you wanted to get a number that is smaller than 3. You roll the dice and you have a chance of getting 2 and win on your first try but if you get something bigger like 5 you have to roll again. You do this
random work of rolling the dice until you get a number that is smaller than or equal to your
target.
That's mining. The only "math" in it is the integer comparison.