What does the silver star in next to the city name mean? I've seen it in otherr civ's cities but I don't know what it's supposed to be.

Silver star city is a city with Forbidden Palace or Versailles

I always wondered why the background to some city names are different colors, I'm assuming it has to do with whether or not the city is growing but I've never took the time to study it.

I always wondered why the background to some city names are different colors, I'm assuming it has to do with whether or not the city is growing but I've never took the time to study it.

If you're talking about the red backround behind some city city names, it indicates cities belonging to civs in war with you (barbs included) .At least I haven't noticed nothing more regarding that.

If you mean the dot with the city number;

green, the city grows.
white, even (no growth, no starvation)
red (starvation, not enough food)

The silver star indicates a secondary capital city, and lowers the maintenance costs of the cities nearby.

Indeed, as stated, the silver star is a secondary capital. This means, as also stated earlier, that it has either the Forbidden Palace (a national wonder that requires a certain amount of courthouses) or Versailles, which I believe requires Divine Right. Why is this shown? You can basically think of this city as an ecomonic stronghold of the enemy, so long as they do not have the State Property civic enabled. If you can take out your enemy's secondary capital, and assuming it is not near your enemy's main capital, then there will be severe economic punishments for your enemy. For example, if you have a secondary capital on a whole different continent, then this will decrease nearby cities you own by quite a bit. If somebody takes this secondary capital from you, then all of the sudden you'll have the pay maintenance costs that reflect the distance from cities that were nearby your now captured secondary capital all the way to your main capital. If this is a large distance, you could see somewhere around twenty or thirty additional gold that will be required to maintain each city. I think that it goes without saying that this will have a profound effect on your technology slider, and your production if your production is demoncracy-based. The quick solution would be to change to State Property, but if you're one to like the other economic civics then you'll be in some trouble.

If you mean the dot with the city number;

green, the city grows.
white, even (no growth, no starvation)
red (starvation, not enough food)

Yeah that's what I was talking about, I figured it was just like you said but I wasn't quite sure