The reaction between vitamin C and iodine is a redox reaction, in which one substance is oxidised (loses electrons) and the other is reduced (gains electrons). In this case, vitamin C is oxidised to dehydroascorbic acid, and iodine is reduced to iodide ions.
The rate of a redox reaction depends on the concentration of the reactants, the temperature, and the presence of a catalyst. In this experiment, the concentration of vitamin C and iodine was constant, and the temperature was room temperature, so the only factor that could have affected the rate of the reaction was the presence of a catalyst.
In this experiment, there was no catalyst present, so the reaction proceeded at a relatively slow rate. However, after 240 seconds, all the vitamin C in the mixture had been used up, and the reaction stopped.