I personally think that the best way to find that out is through experience and not so much thinking about it. However we can have an approach to mindfulness with some concepts and examples.
Mindfulness is being aware of your mind. That means that you pay attention to whatever is going on in your mind. You observe your inner world and become curious about it so you start to develop this attitude of being open to know yourself deeper. It is important to remark that mindfulness and meditation come together. Meditation is the means with which we practice and become a mindful person.
We all have experienced mindful moments. For example, when we are doing something that we love (in my case is dancing)and our whole body and mind become one and enjoy the present moment. If you close your eyes for a moment and bring a memory where you where just enjoying the moment without worries about the future or past, then you have experienced mindfulness because it is something we all have access to.
Nevertheless mindfulness is not just being happy or relaxed, that's just a part of it. Mindfulness is also about embracing and accepting whatever we might be experiencing in our mind and body. For example when we are having a lot of stress, instead of avoiding, fighting against it or feeling guilty about it, we just allow us to feel stressed, we are gentle with ourselves and we don't push ourselves to feel better. Whit some practice and meditation we will develop the ability to reduce stress. As everything, it takes practice.
Science has shown the benefits of practicing mindfulness in many aspects of our lives. To mention some, it can improve our sleep, neuroplasticity and attention. Some studies have shown the effects of Mindfulness-Based Cognitive Therapy (MBCT), part of the work of Jon Kabat Zinn applied to people who have had depression. Mindfulness not only reduces depressive symptoms but it also reduces the reactivity of the amygdale which tends to be very overactive in people with depression.
About the neuroplasticity, Dr. Craig Hassed says that the brain is constantly rewiring itself right throughout our lives. From a therapeutic perspective, it also means that we can ‘unwire’ unhelpful patterns of thought and behaviour and wire in helpful ones.
Mindfulness enriches our enjoyment of life and our power to chose how we want to experience the world. It gives us a choice and another way of thinking. It has been proven that mindfulness helps us to become not only more aware of ourselves but also happier.