If you click "Inventory" on the Personal Menu on the left (probably near the bottom of your options on the left menu), you can see all the stars you've got. On that page, near the top is a link to "Go here to find out more about Inventory in general."
http://www.conquerclub.com/public.php?mode=instructions7 Go check that out, or read more here:
[spoiler]Inventory
For various actions, the Conquer Club deities may smile upon you by rewarding you with items. These items come in different forms, some of which are described below. They will appear in your Inventory. The odds of getting a particular item for a particular action vary.
Where can I get Inventory Items?Currently you may get items by:
•General Activity - If The Conquer Gods smile upon you, you may receive random items just for clicking about
•Joining Games - awarded randomly (or not) when game starts
•Winning Games - awarded randomly (or not) after your victory
•Winning Tournaments - where an item is listed as a prize
•Community Events - watch out for community events featuring inventory items!
What are the odds of winning different Inventory Items?The odds vary depending on various factors such as the type of games you are playing. The most rare Items are very difficult to get indeed. Here are some things that can improve your odds of winning and also increase your odds of winning better stuff:
•Regular games yield better (random) inventory items than Tournament games or Bot games
•Playing in games with more players increases your odds of winning
•Small maps have a reduced chance of winning
Can I see someone else's Inventory?
No - not unless they show you.
Can I swap Inventory Items with other players?
Not at this time.
How can I use Inventory Items?Currently you may use items for:
•Joining Tournaments - certain tournaments will list Items as an Entry Cost
•Sacrificing to the Conquer Gods - perhaps they will reward you
•Staring At - If you stare for long enough at an Item, something changes inside you[/spoiler]