I often see a clock in the upper right hand corner. What time, or elapsement of time, is it supposed to be showing? am confused. thank you.

It's your local time.

after the ammount od ships has been killed, the clock starts, when it hits 0 then the enemy respawn and you can kill them again. So if you enter a fleet action late, you can see how long until it respawns for a new instance of the fleet action.

That is the actual local time you're playing - so when you've been playing for 15 hours and you realise *oh crap - I got to work in the morning..." - you can feel really bad about it

I suspect it tries to display your local time based on your time settings you've selected on your account info on the website. If it's not showing your local time it's probably because you haven't set your timezone info in your account settings here on the website.