"Exactly one" means "one and only one," sometimes also referred to as "just one" or "one and only one." J. H. Conway
has also humorously suggested "onee" (one and only one) by analogy with
iff (if and only if), "twoo" (two and only two),
and "threee" (three and only three). This refinement is sometimes needed
in formal mathematical discourse because, for example, if you have two apples, you
also have one apple, but you do not have exactly one apple.

In 2-valued logic, exactly one is equivalent to the exclusive
or operator XOR,