Note! This quest is optional, but its completion can bring you closer to unlocking next major Companions quest.
Possible quest givers are Vilkas or Skjor. After you agree to complete the task, you'll be asked to rescue a randomly chosen person, held in random location of game world. Leave Whiterun and travel to the place marked by the game. Once you get to the destination (it could be some encampment on the ground or a cave), it will be probably necessary to eliminate fairly large and probably tough group of enemies (screen above). During the fight you should deal with individuals with magical abilities first, and leave the rest of enemies for later.
After the fight, look around to find the kidnapped person (screen above). If this person stays in a public are, you do not have to o anything else. But if the kidnapped person is imprisoned in a cage, you have to open it and you can use lockpicks or a key, which should be found at one of the defeated bandits' corpse.
But that's not all, because you have to safely escort the kidnapped person home. Use the fast travel if possible (screen above), so you do not have to worry about your companion's health. But if this is not possible, then try to use a carriage or travel to the nearest unlocked location and then walk to your destination. Do not forget to talk to the person you've rescued after you reach the destination. You can now return to a quest giver and collect your reward in gold.