One of Four energys used in Tiger's Eye.

Askara's Energy, from Askara the Mist Cat
Aloki's Energy, from Twinhead Viper Aloki
Spike's Energy, from Spike the Impaler
Wally's Energy, from Machine Wally

All of those rare monsters are 1-Star, and using its energy in the magic circle will give a certain buff for 5 mins.
(Spike's -> Stamina, Askara -> Strenght, dont know the others)
Using the 4 at the same time will give a Movement Speed buff for 20 mins (an 8.1 m/s walking speed)

Note: DO NOT expect a reward, doesnt seem to be anything like that, just buffs.