Mindfulness

Mindfulness (Pali sati; Skt. smriti; Tib. དྲན་པ་, drenpa; Wyl. dran pa)

In terms of shamatha meditation, you could say that mindfulness protects and maintains the 'remaining' or stillness (Tib. གནས་པ་, népa) of mind, so you do not become distracted from it.
Mindfulness is the fifth antidote of the eight antidotes to the five faults in meditation practice. It’s the antidote to the second fault, forgetting the instructions or the object of focus.
In the practice of maintaining discipline, mindfulness is defined as "not forgetting what should be adopted and abandoned."

Subdivisions

In the Mahamudra teachings, there are said to be four kinds of mindfulness:

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Ringu Tulku Rinpoche, Paris, Rigpa centre, Levallois, 23-24 May 2001, 'Mindfulness In Everyday Life'