Note! This mission is optional and can be completed multiple times (on average once every couple days). You will get the chance to receive this mission no sooner than after finishing the first main College of Winterhold quest, First Lessons.
Find Drevis Neloren (screen above) who should be travelling through various College rooms, including the main square, Hall of the Elements and Arcanaeum. Speak with him to surprise him that he's visible for you and ask if he needs your help with anything. He will ask you to purify three magical energies and for that give you the Mystic Tuning Gloves.
Open the inventory and equip them in place of your standard gloves. The first magical focal point is on the main square of the College of Winterhold (screen above). In order to cleanse it, just approach it and press E. Keep in mind that you might get hurt during it, so heal up if you do. On the other hand, you can also hope for a random Soul Gem.
The second focal point is in the middle of the Hall of Attainment (screen above).
The third and last point can be found in the central part of Hall of Countenance (screen above). Return to Drevis and inform him of completing the mission, returning the gloves as well.