Earlier quoted context omitted.
I would add the free, short, book "Mindfulness in Plain English". It changed my life. Here is the PDF: http://www.urbandharma.org/pdf2/Mindfulness%20in%20Plain%20E...
What exactly is mindfulness in simple terms? How is different from concentration?
Concentration is much more one of a one-pointed thing. It's about focusing like a laser on one thing. When I'm concentrated it feels like everything except what I'm focusing on drops away. It's like playing a video game, or reading an interesting book. It's a very calm experience, except that sometimes it feels like there is effort involved
Mindfulness is much more about paying broad attention to what's going on, about being aware and accepting of whatever experience is arising in the present moment. There is a strong intentional component -- I want to pay attention to the present moment, and there is an open curiosity and willingness to just be with whatever arises. There is a certain amount of memory involved, too, in the sense that you need to remember to pay attention and not get caught up in your own thoughts.