At its most basic mindfulness is a technique to step back from stress and emotion, to allow yourself to return to rational thought.
Stepping out of your emotional state can be really beneficial in times of stress, allowing you to make better decisions.
Try this quick excersise: try to think about how your body is pushing against the seat/floor right now. Pay attention to the pressure pushing back against you.
Next, try and pinpoint how your body feels when you breath in. What feeling is most vivid? Concentrate on that for a few breaths.
Being actively conscious of your physical state is the first step towards mindfulness. It uses basic physiological sensations to give your mind something neutral to focus on, triggering that step away from feelings of stress and emotion.
Once you have mastered only thinking about your body’s sensations, try and think about how you are feeling. Understanding that you can separate yourself from your emotions is the key, and the more you do it, the easier it gets when you’re in a stressful or emotional situation.
If you want to dive deeper there are lots of resources to help you get started.
Dan Harris: Meditation for Fidgety Skeptics