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A definition always looks something like this:

We say $P$ if and only if $Q$.

Is there an example of a definition where the biconditional is replaced with "if" (and we mean just "if")? What about in the other direction?

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    Yes...that is called Conditional. – 2017-01-20
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    No? In a definition, there's always an expression which "has to be defined". A conditional (something of the form $P\implies Q$) doesn't require that. – 2017-01-20
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    In my opinion, definitions don't deserve to be called "definitions" unless they're of the form of "iff". That being said, many authors _phrase_ definitions using "if", letting it be implicit that they actually mean "iff". – 2017-01-20
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    A definition is an equivalence. It is not a definition if it is not an equivalence. – 2017-01-20
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    if it wasn't an equivalence it would be either impossible to prove that something is a P, or it would be impossible to deduce anything from knowing that something is a P. Pretty useless. – 2017-01-20

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Short answer: Every definition is a bi-conditional, but one direction is vacuous so we omit it for the purposes of logical aesthetic.

Long answer: Think about this in terms of what a definition is which is an assignment of meaning to a string of symbols. A string of symbols, say "$xyz$" has no inherent meaning unless we assign it one. So to say something like "A < something > is "$xyz$" if and only if < condition > " makes sense in both directions, but, because it is the first instance of "$xyz$" one direction in the statement ("< condition > $\implies$ "$xyz$" ") is vacuous because at that instance "$xyz$" means nothing in particular.