This is from a piano score.
I would appreciate it if someone could explain what it means -- which notes I am supposed to play, and on which hand.
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This is almost certainly an error. The lower system seems to be notated in the bass clef, since it has to switch to treble at the end. But the grace notes for the left hand make no sense in the bass clef, since b sharp and c are identical for pianists, and they are most likely intended to connect to the grace notes in the right hand, which they would only do if they were already in the treble clef. The correct version would presumably be to have the clef change before the grace notes.
Kilian's answer is quite true; there is almost certainly an error here. However, in case a more basic level of explanation is needed: Any stave can change its clef any time that it's needed. In piano music, the top stave is usually for the right hand and the bottom for the left, but the performer ultimately has the liberty to use whatever fingering he or she wants.
In this case, the only reason to put a few of the grace notes in the bottom stave must be that the author is suggesting that you play these with the left hand. As Kilian observes, these probably ought to be treble-clef pitches; I'm guessing 4th finger for the first grace note, a G#, would make sense. If you'd rather play those grace notes with your right hand you're welcome to, but you would probably want to play the following eighth notes with both hands, so you'd be moving your left hand to that area anyway.
Given the mistake in clef placement, I wouldn't worry too much in this particular piece if you find fingering indications that seem problematic, but in general, if you find treble clef in the bottom stave or bass clef in the top, it's simply because the right hand has moved so low, or the left hand so high, that a different clef is needed to avoid lots of ledger lines.
This version should answer your question. The treble clef is in the wrong place. Put it in front of the flurry of grace notes, then (if you choose to follow the writer's suggestion) play lower stave notes with the LH, upper stave notes with the RH, as normal.
I suspect the original version was produced in the notation program Sibelius, which makes it difficult (if not impossible) to place the clef where it should be, before the grace notes, if they ARE constructed as grace notes. The solution is to add an extra beat to the bar and construct them as a cue-sized 6:2 tuplet. Note the hidden rest. If this is a bravura phrase, the extra beat probably doesn't sabotage playback too much. If strict tempo is required, we may have to resort to notating a hidden version for playback, a non-playing version for display.