What is "if and only if"?

This means only if a certain event occurs it can only result in a certain outcome.

p if q, means, it is not the case that q is true and p is false.

p only if q, means, it is not the case that p is true and q is false.

p if and only if q, means, 'it is not the case that q is true and p is false, and, it is not the case that p is true and q is false.

That is 'p if and only if q' means, p and q have the same truth value.

It is a biconditional in formal logic. It means that both sides of the conditional entail one another. For instance "x if and only if y" breaks down into "if x then y" but also "if y then x". It works both ways.
It is represented in logic like this: X <----> Y

for example

you can watch TV if and only if the TV is turned on./this is right/

but

you can watch TV if and only if the volume is 15.
/this is wrong, because if the volume is not 15 you can watch TV as well./