The purpose of mindfulness meditation is to develop the habit of being present to what we are experiencing now. Like all habits, it is strengthened through practice. Of course, sometimes we must think about the future or the past, but this should be a conscious choice rather than an unconscious habit.
With time, our ability to be mindful gets stronger so that we can practice meditation without an object. In this sort of meditation we remain aware on whatever arises in our minds without trying to alter in by holding on or pushing away. The advantage is meditation without an object is less artificial and allows us to understand the mind as it naturally is instead of some contrived state. This meditation is sometimes called "doing nothing." This is both true and false, because normally we are always doing something with our minds. Simply observing is unusual. You might object that we are always aware of our minds. Yes, but there are degrees of awareness. Just as we always have some attention on the present, we are also always somewhat aware of our minds, but the degree of awareness can be less or more.