Sati is often found translated as mindfulness or recollection.
It is the seventh member of the noble eight-membered way on the path heading to the cessation of suffering. And it is said of sati that it means memory. It would be handy if a translation could be done by meaning and by letter but memory doesn't quite fit so recollection or mindfulness are used. Now, mindfulness, or awareness, would be sampajañña, see SN 47,2 and SN 47.35, so we can quickly skip that as a valid interpretation. That leaves us with recollection.
But let's look into this a bit more. First textual, by looking at what is called sati (SN 45.8) and then practical, discoverable, by looking at the noble eight-membered way as here these members lead on from one to another. So with recollection for sati we would get:
As to what is called recollection:
'Here, almsmen, an almsman looking into body dwells in body as the ardent aware recollector would be disciplining the avarice and distress about the world ... feelings ... mind ... principles ... This is called, almsmen, right recollection.'
And as member of the noble eight-membered way:
'With right view, right attitude; with right attitude, right speech; with right speech, right doing; with right doing, right way of life; with right way of life, right exertion; with right exertion, right recollection; with right recollection, right concentration'.
And thus would recollection take some justification to make it work; that what is called sati doesn't look like what we would expect to see for what memory is at all and it doesn't flow quite smoothly from the previous member into the following one either. So it doesn't work. Then let's approach sati differently.
What we know is that right exertion enables right sati and right sati enables right concentration. The four radiances (jhanā) are the summit of right concentration and from the second one on thoughts and thinking (vitakkavicāra) are not present any more. And that means that in sati they are. Right exertion creates desire, exerts and applies vigour, strains and confronts the mind for the (non)-arising of (un)arisen (un)wholesome principles. So when right exertion is exerted, what is there then left to do? We can't say 'to stop thoughts and thinking' because that stilling belongs to the next member, so what is left?
Normally we dwell in the world, going after all sorts of interesting experiences. We can dwell in a book, we can dwell in the past, but when not falling for that, then what is there left to dwell in? Body, if what is looked into is body, or feelings if what looked into are feelings, or mind ... or principles ... thus to dwell in one's own domain, that is what is left to do. Suppose someone is reading a book, quite absorbed, oblivious to the world outside. It can happened that when a person calls them they would not hear it. It doesn't mean they don't hear sounds; suppose there was music playing and that gets stopped, this might get noticed even though they where oblivious to exactly what was playing; it just all became background noise. So this person is absorbed while they are seen turning the pages, while the story is very much alive for them; we could call this being absorbed, or dwelling, or living, in the story. But how would you call it when someone sets aside all the avarice and distress about the world, draws back from the outside world, in order to turn inwards into their own domain?
I would call this meditating. Let's see if it would fit the two points:
As to what is called meditation:
'Here, almsmen, an almsman looking into body dwells in body as the ardent aware meditator would be disciplining the avarice and distress about the world ... feelings ... mind ... principles ... This is called, almsmen, right meditation.'
So far it fits nicely;
And as member of the noble eight-membered way:
'with right exertion, right meditation; with right meditation, right concentration.'
Here too it flows smoothly right? That meditation sides with concentration is something even people who don't know anything about the noble eight-membered way might say; it is not strange to see that the training to advance in mind would involve meditation. Right meditation enables right concentration.
It doesn't seem to be the case that sati, in this context, must mean memory. It is not used that way, not in the translations nor in the Pāḷi. I used to find meditation vague 'what is it you do?' but explained as dwelling in body, feeling, mind, principles, so to turn inwards into one's own domain, and by telling what is preliminary done through right exertion 'by removing the avarice and distress about the world' it became quite practical.
So is sati not memory then?
Well, it depends. Usually when we talk about memory we think of it as this thing, just like we do with consciousness. And therefor the descriptions didn't seem to fit. But memory and consciousness as things are just figures of speech. Memory is about the ability to remember. If someone remembers the past, they can relive the past, they can dwell in the past. So memory is this ability to withdraw from the current surrounding to dwell in the past. And withdrawing from the current surrounding to dwell in one's own domain is what we call meditation. It is this mechanism what sati then is (which is what memory then is). Grammatically do memory and remembering for sati not work, and as they are commonly looked at from another angle they are understood as being different things. And as sati is usually translated differently, we then end up with three different things (memory, remembering or recollection, meditation). But we can say that the mechanism of how this ability to remember operates (memory) is, when dwelling into one's own domain, called meditation. Or we can say that memory is this stepping back, and within a certain context is this stepping back called meditation. And so is meditation memory. But to avoid being misunderstood it is better to just use meditation, after all etymology is not exactly what we are after.
Pāḷi-English
Sati (f.) meditation.