what is referred as coin in bitcoin network? I gathered information about bitcoin from various resources. All those resources said that when a transaction is done, the transaction get added to a block. So when Alice send 2 btc to Bob, network checks all transactions having Alice's wallet address to calculat balance Alice has. If he has 2 btc then transaction is happen.

So in this process, system just checks for total balance Alice has. There is no file or a record for each bitcoin. There's only blocks containing transaction data.

But I found about bitcoin mixers. Those mixers claims that they mix coins. That is, when you give them some coins, they will give you same btc amount back but you receive different coins than the ones you deposited. Also I found many websites using the term coin ("coins transfered", "coins recieved" etc.) But I could find what exactly the "coin" means. There are 'blocks' and 'transactions' but 'coins'?

So the question is, what a coin is? Is it something like block or transaction? Is it a seperate file, so that bitcoin mixers can mix them up?

What is referred as 'coin'?
TL;DR: When bitcoiners refer to a 'coin' they really mean a UTXO, unspent transaction output of any amount from 1/10,000,000th of a BTC to 21million BTC.

When someone sends bitcoin to another person, it gets added to the blockchain as you said. When signed by the sender's (Alice) key and verified by the miners, that transaction becomes a new UTXO. 

When Bob goes to spend the 2 BTC that Alice sent him, his wallet will create a new transaction that says, in effect "take the UTXO from X address (that Alice sent him) and transfer it to the following Y address ..." That then creates a new UTXO.

In this example there is simply two bitcoin in each transaction. But what if Bob only spends 1 of the 2 Alice sent him? His transaction will then say "take the UTXO from Y address, send 1 BTC to 'Z' address (his recipient) and return 1 BTC to my wallet at the following 'change address, A The change address, A, is in Bob's wallet, so it can again be spent by him at a later date. In this example, the single UTXO (aka coin) that Alice sent Bob has become two of half the size each. Thus the absolute number of 21 million bitcoin is preserved.