I just came across this term, and interestingly enough, I have been practicing mindful meditation without even knowing that THIS is what I have been doing all along.
Typically when I go to sleep, and especially when I am trying to sleep and I am not at all sleepy is when I mindfully meditate. This really means, that you close your eyes, and allow your mind to engage into each and every sound that you hear around you. Each sound will awaken a memory, or a thought, a feeling, or an action. And you allow your mind to take over and flow through your thoughts. Each new sound will stimulate a new thought. Amazingly, this will put you into a deep meditation, and finally into sleep. The tough part is to control your meditative state, and to not fall asleep, as I have been doing all these years.
It is, "a moment to moment awareness of changing objects of perception", as revealed by Frank Jude Boccio a teacher of yoga and Zen Buddhism and the author of "Mindfullness Yoga".
This type of meditation ultimately teaches us to practice "Upeksha" or "Equanimity" or a clear, and balanced response to the trials of life. As Frank Boccio says, "we are moved by injustice in the world and motivated to make things better, but our deep inner serenity is not disturbed." This is the only constructive way that we can contribute to society in a meaningful way, without each event (such as disaster, war, or tragedy) gaining hold of our inner selves. When that happens, we are unable to think objectively and we may end up acting in a rash or unreasonable manner.
Swami Satchidananda says, "You can't stop the waves, but you can learn to surf". :)