The distinction between contingent and necessary statements is one of
the oldest in philosophy. A truth is necessary if denying it would
entail a contradiction. A truth is contingent, however, if it happens
to be true but could have been false. For example:

    Cats are mammals.
    Cats are reptiles.
    Cats have claws.

The first statement is a necessary truth because denying it, as with
the second statement, results in a contradiction. Cats are, by
definition, mammals – so saying that they are reptiles is a
contradiction. The third statement is a contingent truth becuase it is
possible that cats could have evolved without claws.

This is similar to the distinction between essential and accidental
qualities. Being a mammal is part of a cat’s essence, but having claws
is an accident.

http://atheism.about.com/library/glossary/general/bldef_contingentsta…

A proposition expresses a necessary truth if and only if denying that
proposition would result in a self-contradiction. On the other hand, a
proposition expresses a contingent truth is one which can be
rationally denied without resulting in any self-contradiction. Thus,
for example, the logical principle of the law of identity (a = a) is a
necessary truth because in order to rationally deny it, one would have
to assume its truth (for example, in order to deny it, you have to
assume that it is identical with itself, otherwise what are you
denying?) – a self-contradiction.

http://atheism.about.com/library/glossary/general/bldef_contingenttru…

The necessary/contingent distinction concerns the modal status of a
statement. To say that a statement is necessarily true is to say that
it must be true or that it is true in all possible worlds. A statement
is contingently true in case it just happens to be true because of the
way the actual world is.

Traditionally, there are three "modes" or "moods" or "modalities"
represented by modal logic, namely, possibility, probability, and
necessity.

http://en.wikipedia.org/wiki/Modal_logic