Yes! The quantity that the merchant has available to sell. Unfortunately at the moment it's not automatically managed when an item is purchased, but that will come.
Okay. So when I set it to a value higher than 0 it can be purchased directly? Because I did not set it in my listings and I only can send "Inquiry messages" instead of purchasing directly.
It should be able to be purchased directly on the listing page regardless of a quantity being set or not. You just click on the listing then the "buy now" button.