Refers to a very recent past, similar to さっき but slightly more formal or written. Often used adverbially.
He called just a short while ago.
Please forget what I said a moment ago.
Used to emphasize that something has already happened or been the case for some time. Often carries a nuance of 'as you should know' or 'needless to say'.
That problem has already been resolved.
As you already know, we are closed tomorrow.
already well aware; knowing full well
Compound of 先 (previous, earlier) and 刻 (time, moment). The combination naturally yields the meaning 'a short time ago' or 'already'.