What is this extra item that came with my travel bag?

I guess that you can put a label with your personal information there, so that the finder knows who the bag belongs to in case the bag is lost.

I would agree with what Michael says: it's for your personal badge. Typical usage is that you put inside a heavy-paper card with your name and home address. Typically, you put the name there in such a way that it's visible when the paper is inside (so that you can identify your luggage), and you put your home address in such a way that it's covered (so that nobody can get it easily, but still the luggage can be shipped to you if you lose it).

However, I am yet a bit dubious because these things are usually attached to the luggage quite firmly.

I believe it is a credit card holder, wallet. The slot is there to make it easy to push the card(s) out of the wallet.

I found an example of something somewhat similar that might help confirm my guess.

The main thing that makes me unsure of my guess is the rounded shape... I would expect a credit card wallet to have square corners to hold the cards snug.