Note! This quest is optional, but its completion can bring you closer to unlocking next major Companions quest.
Aela is the only giver of this quest. After you agree to complete the task, you can be asked for one of two things. A first variant is that Aela wants you to get rid of random monster or beast, who can reside in his lair or in some house in Skyrim (random). Leave Whiterun and travel to the place marked by the game. Once you get to the destination, deal with the beast or monster (screen above).
A second variant is to clear the entire lair of beasts or monsters. Also in this case you have to leave Whiterun and travel to the place marked by the game. A basic difference now is that you hate to get inside the lair and kill all beasts or monsters present there (screen above). Regardless of your instructions, return to Aela after the fight and collect your reward in gold.