I'm pretty new to crypto and I'm confused about POW
POW Is usually explained like this...
A group of transactions are bundled into a memory pool (mempool).
Miners verify each transaction in the mempool is legitimate by solving a mathematical puzzle.
How does solving the mathematical puzzle (finding the hash for the nonce) have anything to do with "verifying" the transactions? Isn't the the hashing puzzle just to keep miners from spamming the network? Thus, requiring work (and time to pass) to earn block rewards? Maybe I'm wrong here, or getting confused but isn't the verifying of transactions a function of signature verification with the public key? What does that have to do with the hashing puzzle??
When people say POW "secures" the network, what do they actually mean?
The first miner to solve the puzzle gets rewarded with newly minted bitcoin (the block reward) and network transaction fees.
The verified mempool, now called a block, is attached to the blockchain.