Quote from: Davidvictorson on Today at 07:55:41 AM

Sometimes, when I click to check, I see a lot of addresses. I have a vague idea that it is for processing the payment(correct me if I am wrong). The question I have is: how are the payment transactions processed? What actually goes on there?

If you look at the link you dropped to the multiple transaction, you will understand that everything is self explanatory.
Let review it with pictures...

The above picture shows these important information.
The transaction ID,
The total amount that was transacted,
The transaction fee,
From whom and to whom. (It does not necessarily need to be from one address to another address. It can be from one address to many, from many addresses to many, in the case of the above example)
The status of the transaction and the block information.

This second image shows in full the number of wallets involved and to how many it sent the transactions to and including change address for balance brought back. It is here you will also see how much was spent from each wallet and how much sent to each wallet.

That is the beauty of the blockchain and the information is there forever and open for you to see but cannot be mutilated.
Incase you may be confused about the type of address seen there which uses names in it, it is called a vanity address.