Why and how should I be mindful of my thoughts?
Unless we're aware that thoughts are happening, then usually we’re just driven by them. Sometimes you'll hear them referred to as the “little dictators” in the mind. As you start to pay more attention to your mind, you get familiar with your mental habits, like the tendency to get distracted, lost in fantasy or worry, or caught in recurrent emotions.
With practice, it gets easier to notice when you're lost and to gently bring awareness back to whatever it is you want to be paying attention to. This needs to be done with patient, kind persistence though, because trying to force your mind to focus or be more disciplined is often counter-productive. Repeatedly and gently bringing your mind back to simply being present with experience is what develops the kind of focus and discipline you’re aiming for.