I don't play piano, but I'd like to learn how, so I picked up a beginner's method book to start teaching myself (Carl Czerny - Practical Method for Beginners on the Pianoforte; edited, revised and fingered by Giuseppe Buonamici). In the book, when one note is played twice or more in a row, the fingering written above the note changes. Is there a reason for this that I should know about? It confuses me since it would be easier (at least by my logic) to keep the same finger on the key to play the note both times.

I had the same question as you previously. I asked my piano teacher and he says I don't always have to follow the fingering indicated in the book. So I just stay with the same finger for the same note if it's easier / more comfortable to play that way. I change the fingering (for the same note) only if it makes it easier for my other fingers to play some other notes further down the bar.