Mindfulness meditation is about cultivating awareness and can be practiced in two ways, formally and informally.
Formal meditation is akin to going to the gym to build muscles. By sitting and paying attention to your breath and bringing your attention back to your breath whenever your mind wanders off allows you to cultivate your ability to attend and develop the muscle for paying attention and becoming aware of what is happening in the present moment. When you sit you are not trying to achieve a particular state of bliss, or trying to block thoughts or control the mind. You simply sit fully aware of your breath, feeling it as you breathe in and out. Sitting with yourself allows you to connect with your being and teaches you how to simply be with your thoughts, emotions, bodily sensations while adopting a non-judgemental attitude. Such an approach promotes an attitude of openness, acceptance, and gentleness toward yourself and others.
Informal meditation is about practicing being present to what is happening in your daily life. This can be practiced by simply paying attention to what you are doing moment by moment adopting an attitude of curiosity, as if you never experienced what it is that you are doing, essentially adopting what is often referred to as a beginners mind. For example, when you take a shower in the morning, you take the shower as if it is the first shower taken after spending a month camping in the desert. Bringing your attention to the sensation of the warm water flowing on your body, the smell of the soap, the sense of wellbeing that slowly emerges… Try adopting a beginners mind to the tasks you encounter over the course of your day, what do you notice?