Curiosity is an important aspect to mindfulness practice. Each moment is a new moment in time and space. To fully encounter the moment without coming to it with a lot of preconceptions and the thought that we already know what it is, can be best done with a sense of curiosity and investigation. When we are curious about the fullness of each moment, we might find that there are things about each experience that we have not noticed before. In essence, we are changing our view and our vantage point and entering into the moment just as it is. Since each moment is a new moment and a fresh moment, we can intimately engage with the moment-to-moment awareness that is the foundation of our lives.
Curiosity also means recognizing how our preconceived ideas and perceptions tend to be how we are when we are stuck on autopilot for a lot of our experiences. When like this, we may miss an opportunity to be intimate with our lives. One of the things that we may recognize is that it is almost impossible to come to any experience without looking at it from a particular lens. Even the physical mechanics of sensation and perception means that we are always interacting with things through a filtering process. Curiosity allows us to see through the lens of perception and see things how they really are from moment to moment. We can bring this curiosity to our present moment by asking questions like: "What is here right now?" "What has entered the field of awareness, just now?" "What is this?"
The way that this practice affects our lives when we are making an effort to live mindfully through the foundation of curiosity, is that we see our lives just as they are from moment to moment; and we recognize the way that tightly held ideas and opinions about reality often separate us from the immediacy of what is right in front of us. In fact is not even right in front of you, it is you through and through. Then perhaps we can engage life fully in all of its beauty and all of its messiness.