Buddhists are very mindful of their own thoughts as if they were dangerous, cracked-out squirrels.
Mindfulness is actually pretty useful. What it means is "paying attention". However if you write a book on paying attention, no one is going to spend twenty dollars to hear what you have to say. Now if you market it with a title that sounds like something Master Yoda or Emperor Palpatine might say, you're going to at least pick up the geek/nerd disposable incomes.
As previously stated; mindfulness means to pay attention, usually to one's thoughts/emotions/physical feelings. This is important because by paying attention to how these things arise and pass away, one can see that they are impermanent. If one knows that a thought like "Wow, I'm a useless schlub." is just a thought that arose from somewhere (probably a failure in a relationship or job or some other cause) and is going to pass away, one is less likely to dwell on it and let it fester causing one to go nuts in a McDonalds and hurt people. One sees the "Wow, I'm a useless schlub" thought and pays attention to its causes, deals with the causes, and then notices that the "useless schlub" thought passes away.
This is how mindfulness is supposed to work. It's a problem solving device. It takes concentration and effort. It's also not an end in itself. Just sitting on your backside on a cushion, paying attention to your thoughts as they pop up, is not going to really accomplish much. After you see the sources of problem thoughts and accept them, finish up your meditation and see what you can do to improve them. Then you're actually on a path to ending a bit of your own suffering. That's Right Effort, Right Mindfulness, and Right Meditation!