What's this mean?

[smoky dome]

parity ^= (1 << root.val); // Toggle the bit at the position of root.val

[placid anvil]

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[gleaming jasper]

<< means left shift

1 << something is essentially equivalent to 2 to the power of something

or in binary, a 1 followed by something 0s

then ^ is XOR

and ^= is XOR+=
i.e.

a ^= b;

is equivalent to

a = a ^ b;