What is the idea behind ^= 32, that converts lowercase letters to upper and vice versa?

Let’s take a look at ASCII code table in binary.

A 1000001    a 1100001
B 1000010    b 1100010
C 1000011    c 1100011
...
Z 1011010    z 1111010

And 32 is 0100000 which is the only difference between lowercase and uppercase letters. So toggling that bit toggles the case of a letter.