From: Money and Value 4
Right recollection, right mindfulness. We're going to have to retire the word mindfulness. It's been hopelessly corrupted in English. Its fundamental meaning is to remember. To remember where you are and what you are doing. That's what mindfulness means. The word in Tibetan, Sanskrit and Pali means to remember. So I'm not sure where mindfulness came from English-wise. But it did.
It's constructive and helpful to remember. And there are certain things that is not constructive and not helpful to remember. Wallowing in the memory of things still done and done to others harm and things that were done to you is not particularly constructive. It reinforces a whole bunch of tendencies etc. So there's a way of practicing mindfulness or recollection which is beneficial. That's what right mindfulness is.
Note: More on mindfulness in: A Trackless Path II, 5 Eightfold Path 2,