I have read several blogs and several small books but none of the book could explain easily how does exactly a bitcoin generated. I know the following things:

1. After every 10 minutes, a block is generated which contains all the transactions that happened since the last block got verified.

2. All the miners try to verify the newly generated block. It's a hard mathematical problem which requires extensive computation. The miner which solves that problem gets 12.5 Btc in reward.

I am confused about that mathematical problem. What is that? Is it finding a key by brute force method for the newly generated hash of the newly generated block? Why is it so hard? Is it because the hash generated becomes longer and longer as the number of transactions have increased? Or is the hash generated contains all knowledge of the transaction since the first bitcoin generated?

Can some one explain me in simple terms? I want to make other people understand the value of bitcoin but get confused myself while explaining them.

P.S. I am a technical person and have no difficulty in understanding the mathematics.