... it is basically a process through which blocks (that contains information about transactions) are verified. For that miners has to perform simple calculations Nodes (Computers) does that for miners. The one who performs it the first gets the reward .Thats how all the blocks got mined!
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To understand mining I suggest you consider two different aspects:
a) Why is mining necessary at all. What is the purpose of mining.
b) What is the process of mining.
The (b) part is only relevant for developers or people who need to actually act on the technical level. As you say, it is related to solving a computer intensive problem with the best result (the one with more "work") for a given block.
The most interesting part is actually (a). Mining is a process that secures the Bitcoin network. It is mainly designed to avoid any malicious actor to be able to tamper with the network and it is IMO the greatest achievement of Blockchain.