What are these holes in my Cessna 172, just in front of the elevator?
Those are called "Lightening Holes". The name refers to the weight reduction brought about by removing part of the material—lightening—and should not be confused with anything to do with electrical discharge—lightning.

From the FAA's AMT Airframe Handbook, in Chapter 4, page 4-82:


  Lightening holes are cut in rib sections, fuselage frames, and other
  structural parts to decrease weight. To avoid weakening the member by
  removal of the material, flanges are often pressed around the holes to
  strengthen the area from which the material was removed.


The particular part depicted in your photo is the left hand rear spar assembly for the horizontal stabilizer, No. 32 in this figure from the 1975 Cessna 172 Illustrated Parts Catalogue (IPC):



As you can see, these lightening holes are present throughout much of the spar and rib structures in the horizontal stabilizer, as well as the vertical stabilizer, wings, and fuselage.

In addition to the gains in weight reduction, lightening holes also serve as openings to allow the routing of electrical wiring, control cables, hydraulic tubing, and other system components. If you look at the same location on the right side of the horizontal stabilizer, you should see the elevator jack screw passing through one of the lightening holes, in the location marked "C" in the Cessna IPC figure above.