What is sati? Whatever remembrance following after, re-remembrance, act of remembrance, memorization, not shifting or floating, non-forgetting, faculty of remembrance, power of remembrance, right remembrance - this is called satindriiya (the faculty of sati).
It is called sati because of the meaning of remembrance - this passage gives the intrinsic nature of sati
It is called remembrance following after because of the meaning to remember often or remember in the present. The condition of remembering is called the act of remembrance.
It is called memorization because of the meaning of being the ability to memorize those things one has seen or heard.
It is called not shifting or floating because of the meaning of being fully set, plunged into its object.
It is called non-forgetting because of the meaning of not mistaking or forgetting in regards to the things one has done, or the speech one has said, even though it may be long ago.
It is called a faculty because of the meaning that it is dominant in regards to the characteristic of appearance.
It is called the power of remembrance because of the meaning of not floundering in regards to its object and because it is not negligent.
It is called right mindfulness because of the meaning that it is able to lead one out of suffering. One should see sati as being like the supporting pillar of a dam, because it is firmly set in its object, and like a a door-keeper because it guards the eye-faculty and so on.
The lakkha.naadicatuka of sati-cetasika:
Characteristic: the ability to remember
Function: not mistaking or forgetting
Fruit: fixing on its object
Proximate Cause: strong recollection or the four foundations of remembrance
yaani sotaani lokasmi.m sati tesa.m nivaara.na.m
Whatever streams in the world there be, remembrance 'tis that stops them all.
-- The Buddha