So my question is, what is the link between these 2 things? If nodes in the network are enough to verify transactions, why do we need miners?
Suppose Alice forms two valid transactions, one sending a bitcoin to Bob and another sending the same bitcoin to Charlie. Without the miners, how can Bob or Charlie ever know which of them gets to keep the bitcoin?
And you might think that if Alice does that, well, neither Bob nor Charlie will assume they get to keep the bitcoin and Alice just played herself. But that won't work. Say Alice is buying a phone from Bob and Bob only sees the transaction giving him the bitcoin. Without the miners, how can Bob be assured that nobody will ever see a transaction from Alice giving that same bitcoin to someone else and decide that Bob didn't get a bitcoin from Alice. How can Bob ever send Alice her phone if he can never be sure the transaction to Charlie will never be accepted by anyone?
When do miners enter in the game of validating transactions?
Miners produce a blockchain that eventually contains only one of those two transactions, allowing Bob to know for sure that he will get the bitcoin from Alice and nobody else will.
And how come that to verify transaction is relied with to find a nonce?
It has to take some significant amount of work to build valid blocks, otherwise a massive number of valid blocks could be created and Bob would never be finished trying to figure out which of them would be accepted. By making it extremely expensive to create a valid block, Bob only has a small amount of work to do and an attacker can't create large numbers of valid blocks to stymie him.
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