i get lots of kills and acationally hear i got an ACE. What is that?

It means the entire enemy team is dead. you can press tab to see their death timers and how soon they'll rez. This would be a good time to try to kill a tower.

An ACE is when you defeat an entire enemy team - IE: They are ALL dead at the same time.

This is different from a Pentakill. A pentakill is you killing all 5 champions in a short period of time. Ace is when ANYONE from your team kills any # of champions then you get the last kill, putting them all back at the spawning pool.

Isn't there extra gold for scoring the ace?

Ace means that the whole other team has died and all are dead respawning but says it to the last person who killed the last enemy, so you could kill the last 3 people or just last one and it will say ace.