While traveling with a overnight flight, I was given a moistened, warm tissue during the flight (it was a night time long distance flight). That was my first long distance (several hours) flight.
I did not know what to do and returned the tissue later when they came to collect them.
What are these tissues and what are we supposed to do with them?
These are for washing your hands and/or face, often after the in-flight beverage, snack, or meal.
On some Asian airlines such as Korean and JAL you will be given real hot towels shortly before each meal. Just like in some Asian restaurants.
This is for cleaning your hands. I've never been sure whether I should also use it on my face, either in a restaurant or plane. I have done so and it's very refreshing, but I'm not sure if the Asians also use it that way or find it vulgar or disgusting.
I think the tissue is a version of this. They are related to "baby wipes" or "pre-moistened towelettes" like you might get in a takeaway pack from KFC. I believe they used to use an alcohol-based solution but many have moved to a non-alcohol based one. Some people are opposed to at least some types of these because they are not biodegradable and contribute to pollution in places where they are very popular and/or not properly disposed.