Thanh V. Huynh, M.D., defines mindfulness this way:
A mental quality that remembers to be present. By paying non-judging attention to all aspects of life, whether pleasant, unpleasant, or neutral, one develops insights into its ever-changing, unsatisfactory, and impersonal nature, facing ups and downs with more equanimity and experiencing less stress and confusion, more joy and peace.
Mindfulness is most often achieved by the training called meditation: focusing the mind on a single object so that it becomes quiet and peaceful. On this subject, Wikipedia says as follows:
However, mindfulness does not have to be constrained to a formal meditation session. Mindfulness is an activity that can be done at any time; it does not require sitting, or even focusing on the breath, but rather is done by bringing the mind to focus on what is happening in the present moment, while simply noticing the mind’s usual “commentary”. One can be mindful of the sensations in one’s feet while walking, of the sound of the wind in the trees, or the feeling of soapy water while doing dishes. One can also be mindful of the mind’s commentary: “I wish I didn’t have to walk any further, I like the sound of the leaves rustling, I wish washing dishes wasn’t so boring and the soap wasn’t drying out my skin”, etc. Once we have noticed the mind’s running commentary, we have the freedom to release those judgments: “washing dishes: boring” may become “washing dishes: washing dishes”. In this example, one may see that washing does not have to be judged “boring”; washing dishes is only a process of coordinating dishes with soap and water. Any activity done mindfully is a form of meditation, and mindfulness is possible practically all the time.