The last part of the experiment compares the rate of a previously reacted mixture (I used the one from the very first reaction with oxalate) with that of a fresh mixture.

The result is counterintuitive. Since the previously-reacted mixture has less oxalate than the fresh one we might expect the rate to be smaller (the purple permanganate is the limiting reagent in all of these so there is still oxalate left, just less than originally). But the "used" mixture actually reacts faster! This is not typical behavior but it is interesting and that's why we are looking at it. A quick check on the overall reaction reveals what is happening here:

5 C₂O₄^2- + 2 MnO₄^- + 16 H⁺ → 2 Mn²⁺ + 10 CO₂ + 8 H₂O

The reaction produces the very ion that we used in an earlier trial as a catalyst!! Such a species is called an "autocatalyst" (or self catalyst). So when we try a second reaction with the mixture it is as if we added some catalyst first.