In simple terms, mindfulness is the ability to be present, or focused, on the current moment. This includes the things happening around you, and within you.
To maybe make it even simpler, it's the ability to be able to not be on autopilot in our day-to-day lives, which most people are on.
Most people just live life and go through their days reacting to the events that occur, but while you are mindful, you are not on autopilot, and you are not just reacting to what happens, you are more prepared to accept what is happening, and are better able to understand it and make better decisions.
When we are on autopilot, many times we just instantly react to what ever happens or to what ever is said. When we are mindful, we let it sink in, we understand it, and then we can better know how to proceed.
It allows us to live a calmer and more peaceful life, with less stress and anxiety, and a better acceptance of ourselves, the people in our lives, and the world around us.
It helps us to not be stuck and focused on the past, or the future, but to be focused on the present moment, on the now.