Luck

Effects

Know Effects

• Summoning: +5% yield
  
• Exploration: +10% to average land explored (info comes from game code, Paralytic 21:37, 23 August 2014 (CEST)

Used to allow for some item generation since guilds postresearch before skills were introduced were worthless outside of random item generation so top rankers generally didn't keep any. No idea now since I'm not going to create a mage on another server to verify (5/30/2011).
Luck from a God may have an additional effect now since I noticed this for the first time this reset (5/30/2011) in my battle reports... "Good fortune shines upon Malbec (#31)'s armies."

Confirmed 8/12/2012:
  5% extra summoning
  5% extra concentration (for casting off/opposite colors/dispelling)
  2% item generation

Speculated Effects

• Chest/Map/Bottle: Increases chance of item generation
  

Bad Luck

You can also get Bad Luck from gods' disfavor. Example of message in the donation screen after donating :

You sense a heavenly conflict between Mr. Satan, the Ruler of Nine Hells and Moon, the Light in the Night.

You hear roar in anger. You are now disfavoured by Moon, the Light in the Night.

Moon, the Light in the Night cursed you! The Star of luck begins to avoid you.

In the Status screen you can also see this message for 24 hours :

Your realm hides in fear knowing you have scorned Lady Luck. You feel that you will regret playing today.

Effects : Summoning: -5% yield

Notes

Star of Luck from different sources stack.

Sources:
Vote (use the link "Vote for our game" on the top of your main screen)
Wish
God Favor