Mindfulness meditation is the practice of turning your attention away from distracting thoughts toward a neutral, present moment, single point of reference (for example how it feels to breathe, sensations present in the body, nearby sounds, feelings of compassion, etc.)
Far from emptying your mind of thoughts (which is impossible), during mindfulness meditation, we practice paying attention to what 𝘸𝘦 want to pay attention to, rather than letting the mind go off on a tangent about thoughts of (a real or imagined) past or future.
Think of the practice as mental reps for your brain. Over time, the more you notice the tendency of your mind to wander off on its own merry way, and gently (but firmly) guide it back to your present moment point of focus - over and over and over again - the better able you'll be to stay connected to the present moment even when you're not meditating.
And that's when the real fun begins...