Indicators show your current astrology modifiers. They can be engineered, bought from players, or bought from Urania in Arius City. To see the modifiers, you must "use" the stone, after which the stone will disappear. In general, a green bar means "good", and an orange bar means "bad". They are a good leveling item for Engineering as they can be sold back to Urania. If you want to know how your modifiers will change in the immediate future, you can buy the respective predictor.
The astrology indicators currently in the game are: