Now before you say 'duh miners of course'
Well, that is the answer to the question in the Subject line of your post.
I would like to ask , when people mine, they get what? 12.5 bitcoins per block? 25 btc? whatever, they get something from the 'unmined bitcoins' part.
Currently there is a 25 BTC per block subsidy of brand new bitcoins that are available when a block is solved by a miner or pool. If the block is solved by a pool, then those are split up into tiny pieces and shared by all the participants in the pool.
Why do we also have to pay them certain amount to send something to other people?
You don't have to. But if a miner (or pool) is choosing between either confirming your free transaction, or someone else's fee paying transaction, which one do you think they are going to choose? If you were a miner and you had to choose between confirming a transaction that wasn't going to earn you any extra revenue, or a transaction that would increase your revenue, which one would you choose?
If we have to pay something for the sake of involving in a technical detail which I am too far away of understanding, why are we not paying just 1 satoshi?
Pay whatever you want. Bitcoin is a voluntary system. If you want to pay a 1 satoshi fee, go ahead. If a miner wants to ignore your cheap transaction, and confirm one that will earn them more revenue, they are free to do so. You can't force them to choose yours, and they can't force you to pay a higher fee. You decide how quickly you want your transaction confirmed, and then provide an incentive to the miner to choose to confirm your transaction.
Considering all the transactions everyday all day, miners probably started to make more money from miners fee rather then mining unmined coins.
Nope.
Average sum of transaction fees per block is
0.3125 BTC (or about $140 at the current exchange rate).
Block subsidy is
25 BTC (or about $11,250 at the current exchange rate).
Then that reward (25 BTC + 0.3125 BTC) is split up among hundreds or thousands of miners.
4 cent could be little for one person but when all combined in everywhere, it is huge.
Sure, but if you are paying more than $11,000 worth of equipment, electricity, cooling, and maintenance per block that you solve, and the block subsidy is only worth $11,250, then that extra $140 worth of transaction fees increases your net profit per block from $250 to $390.