In order to make progress, it is necessary to stress the body above a certain threshold [the event], making it work harder than normal. However, when such an event takes place, energy resources become depleted, and it becomes important to rest.
After such an important event, the body will go through a recovery period, followed by an enhancement period, and it is at this point of enhancement that you should train again. This is important.
If you train before the enhancement period, you will be depleting energy resources further, not improving fitness.
If you train after the enhancement period, you will only be maintaining your current level of fitness, not improving it.
If, however, you begin to train again at the point of enhancement, you will be able to improve your fitness further, making advances and adapting accordingly.
Thus, a rest period is important, but understanding the fluctuation of that rest period is more important, being able to identify the point of enhancement, and train accordingly. Keeping a record of your recovery could be advantageous, which will help to maximize your training program, improving your overall fitness.
It is important to note that people recover at different rates, contingent upon individual fitness and length of training session, for example. Being intuitive, and realizing your own point of enhancement, to train again, is a skill to be acquired.