When click on gold givent at top right of screen, what is efficiency?

The screen that shows your gold store will give your current production rate. To increase this you need to upgrade your mint buildings and if possible station and upgrade heroes that help improve this.

The gold also has an efficiency which will affect the production rate. The efficiency depends on 2 things, Charcoal (if you run out then your production rate will drop) and also population. As you upgrade the mint production levels you will need to have a minimum level of population in your town to support the production. If the population falls below this level then your efficiency will go down. To add population build and upgrade houses and keep the Tavern stocked with food and water. If the food and water levels run out your population will drop.