On some arenas we can set an hour online limitation, which means you can only play x amount of hours per rolling 24 hours.
Ferion can become very intense, and sometimes players break their sleep cycles just to take care of their empire. This is not healthy. Also, spending more time on the game gives you an advantage against players that can invest less time because of other commitments.
Lets say the limit is 16 hours. This means for over a period of 24h, you can play 16 hours. This is a rolling 24h, so we are looking at the last 24h from the current time. If it is 8am now, the last 24 would go back to 8am yesterday.
You can see you current status by clicking on this icon at the bottom bar.

The modal will show you how many hours you have left, when did you use them and you can get an idea when new hours will become available.

Any action that changes anything in the game will trigger the hour as "used". For example. Moving ships, changing anything on a planet, giving a spy an order.
Just browsing around your game. also chatting does not trigger an hour.
The hour switches at minute 0. So if you play 10 minutes, and those 10 minutes are from 8:59 until 9:05, you used up 2 hours.