Well you obviously can't have the server running if you're computer is turned off.
Some people just have a separate computer running that hosts all of their servers, whether it's Minecraft, AoS, whatever...

And believe it or not, leaving your computer on all the time isn't that uncommon. I wouldn't recommend it though, you're wasting a lot of energy and kilowatt/hours add up.

In server lists some servers are switched on all time. How do you make so? Is it a special program or you never switch off your computer?