Here's a guide to all Racial Relationship types, and what they mean for those who are new to the Galactic Civilizations Series, or a refresher for old players. This is catagorized from worst to best relationships.
Permanent War- You hate each other so much that the only way to settle your differences to have only one of the two or more civilization be the soul surviver. You can't make peace treaties, nor never trade with that civilization(s). Worst possible relationship status. This must be set in the beginning of the game, as you can never have any civilizations at this status of warfare once the game begins...
At War- Mean's just that. You are at war with that civilization and they can destroy each other's ships, and conquer each other's planets.
Hostile- A grave situation of war may arise when relations are this bad. If they are you better tribute up to that civilization if you don't have a strong enough military, or if your military exceeds there's then you will be ok, as the AI doesn't tend to declare war on you if your military matches or exceeds there's. Your not at war with this civilization and can still trade with them, but keep an eye on your's and there's military stats and try to improve relations, or not. The choice is yours.
Wary- Not in dangered of going to war, but relations are slipping away between yours, and the other civilization. Watch yours and the AI's military might, otherwise you might find yourself in troble later on.
Cool- Means just that. Relations aren't great, but they are that bad. A tribute would quickly get this back up to neutral or warm relations in a few clicks, depending on the size and strength of the tribute. Make sure your military might being less then there's is the cause and try to keep up with them militarially.
Neutral- Relations are just that, neutral. No better way to describe it. Your relations with a civilization start here, unless you have specified in the custom game settings and when you select a race in the start of the game, you can choose what relations you want with the other civilizations from the start!
Warm- Relations are fairly good. The civilization, isn't just going to declare war out of the blue. A good tribute could get this higher into Friendly and eventually close which then you can make an alliance!
Friendly- Good relations. The opponent race generally accepts you, and will occassionally try to help you in some wars and tough times by offering tributes, or even starships, and surrender should that civilization fall by another civilization. Your not first picks for these, but you might get them.
Close- Very good relations. Your practically allies, but not formally. The civilization will help you out most of the time, by coming to your aid in wars, larger tributes, and better ships and technologies. An alliance can be offered at this relationship status. Which leds us to our next catagory.
Alliance- You and the other civilization are bonded by an official agreement to help each other. If they declare war on a civilization, then you will too automatically, unless you have an alliance with that civilization as well, then it will do nothing and you'll remain neutral between them. If your ally dies or falls then you get first picks to who he surrender's to. Which means if your his only ally you'll more then likely get surrendered to, and hench gain your allies empire!
Team- Just means that civilizations are teams and have to work together with each other to reach a common goal. Think of it as a mandatory alliance, but I've heard that the AI occassionally "turns" on it's team, but this is rare...