How can "coins" be uniquely identified?

[hyena_face]

I was reading some papers about Bitcoin and one of the things I don't understand was about the way that coins are transmitted.

For example:

"Bitcoin Laundry twice sent us our own coins back, indicating that we were possibly their only customer at that time."

And:

"...by mixing the coins of multiple users making it harder to find a relation between input and output transactions in the transaction graph."

And:

"there needs to be enough users and bitcoins in the mix otherwise the same coins might get payed out that the user just payed in."

I do not understand what "coins" mean in this context. Transactions, as I understand it, transfer BTC from one person to another as depicted by the blockchain.  How can the specific coins in these transactions be identified?  How, for example, did the reearchers know that they received their own coins back?

I am far from an expert so please write in a simple way!

Thanks.

[Authentic]

Anyone can view everything that happens in the network. A bitcoin payment involves taking coins from one or several inputs (the source) and transferring them to one or several outputs. The amount transferred is substracted from the balances of the input(s) and added to the output(s) balances, and any fees paid are kept by the miner of the block the transaction is included in.

That means that, after paying, you can "follow your money" by seeing the inputs and outputs of each transaction.

[hyena_face]

So, in other words, "coins" just means the addresses that transactions are sent from and received by.

If Address A ----> Address B ----> Address C then we could say that we can see in the blockchains that coins have been transacted from A to B to C.