The Origin and Meaning of "Mindfulness"

The word "mindfulness" is used to translate the ancient Pāli word sati. But what do we mean by "mindfulness" and is it the best word to describe this quality?

"We can bring other nuances out of the term 'sati' in the original language that are not immediately present in the word 'mindfulness.'"

"In some ways, mindfulness is the practice of remembering to be present."