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This is an except of bars 47-50 from Beethoven's "Moonlight" sonata, from the Henle edition.
In bar 49, in the middle of the second triplet, there is a fingering of 2-1 (pressing with finger 2 and switching to 1 while pressing), which I don't understand. Why do they suggest that?
They are assuming you are using finger 4 on the top D#.
The reason to switch from 2-1 is that if you ended up with 3rd finger on the G# and 4th finger on D# above, it is too far of a stretch. If you are playing the high D# with 5th finger it won't feel so uncomfortable, but then you can't connect the melody notes with finger legato. The finger switch allows a move from 4 to 5 in the melody to make it legato. You can obviously overcome the difficulty with pedal, but in my opinion, this piece is often ruined by overzealous pedaling.
I don't think it has to do with legato, at least not in the way ecline6 suggested, because if you're using 4th finger for the top d#, the f#-d# stretch would still be a problem (at least it's for me), and the switch should be marked on the first beat instead of the second. In fact, the only working fingering for using 4th on d# I can think of is to use 1-1-2 for the triplets.
Instead, I think the reason is that if you play g# with the 3rd finger and want to keep the triplets legato, you might have tension in your hand when you play the e octave. With the switch that doesn't happen. Still, it seems to be unnecessarily complicated. Just use the pedal and make sure you don't swallow or accentuate the g#.
Btw, the reason people use lots of pedal is probably because that's what Beethoven wrote! In the beginning it says sempre pp e senza sordini, which means all the time very quiet and without dampers (i.e. with the pedal down). On a modern piano you have to change the pedal at least partly every now and then, though, since the sound is longer. You actually get a pretty cool effect if you, for example, don't switch the pedal at all during the first two measures.
