The mathematical expression of "logically equivalent". In mathematics, logical equivalence is of utmost importance; every logical equivalence is another tool for a mathematician to use in any given problem. "If and only if" is commonly abbreviated iff, because many mathematicians are lazy. For statements a and b, a is logically equivalent to b exactly when a iff b.
Here is a truth table showing the truth values of the statements a, b, a -> b (a implies b), b -> a and a <-> b (a iff b):
a | b | a -> b | b -> a | a <-> b
-----------------------------------
T | T | T | T | T
T | F | F | T | F
F | T | T | F | F
F | F | T | T | T
Mathematicians like iff statements when they are true. For example, let k be a positive integer. k is prime iff k has no divisors other than itself and one (one not being prime). Implications are fine and dandy, but iff is better because then two statements can be interchanged exactly. In some cases, whole classes of mathematical thought can be exchanged directly for each other (see Fermat's Last Theorem, modular forms and elliptic curves).
Some "common" logical equivalences: