A biconditional statement means that the statement and its converse are both true.
If both of the following statements are true,
If he is alive, he respires.
If he respires, he is alive.
then we use the single following statement to say the same thing:
"He is alive if and only if (iff) he respires" which means that the converse is also true:
"If he respires, he is alive".
So being alive is a "necessary and sufficient condition" for "respiring".
See
http://atheism.about.com/library/glossary/general/bldef_biconditional.htm
for more examples and explanations.
what is a biconditional statement
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